Real Space Dimensions Research Articles

Advanced modeling of materials with PAOFLOW 2.0: New features and software design

Recent research in materials science opens exciting perspectives to design novel quantum materials and devices, but it calls for quantitative predictions of properties which are not accessible in standard first principles packages. PAOFLOW, is a software tool that constructs tight-binding Hamiltonians from self-consistent electronic wavefunctions by projecting onto a set of atomic orbitals. The electronic structure provides numerous materials properties that otherwise would have to be calculated via phenomenological models. In this paper, we describe recent re-design of the code as well as the new features and improvements in performance. In particular, we have implemented symmetry operations for unfolding equivalent k-points, which drastically reduces the runtime requirements of first principles calculations, and we have provided internal routines of projections onto atomic orbitals enabling generation of real space atomic orbitals. Moreover, we have included models for non-constant relaxation time in electronic transport calculations, doubling the real space dimensions of the Hamiltonian as well as the construction of Hamiltonians directly from analytical models. Importantly, PAOFLOW has been now converted into a Python package, and is streamlined for use directly within other Python codes. The new object oriented design treats PAOFLOW’s computational routines as class methods, providing an API for explicit control of each calculation.

Structure-preserving vs. standard particle-in-cell methods: The case of an electron hybrid model

We applied two numerical methods both belonging to the class of finite element particle-in-cell methods to a four-dimensional (one dimension in real space and three dimensions in velocity space) hybrid plasma model for electrons in a stationary, neutralizing background of ions. Here, the term hybrid means that (energetic) electrons with velocities close to the phase velocities of the model's characteristic waves are treated kinetically, whereas electrons that are much slower than the phase velocity are treated with fluid equations. The two developed numerical schemes are based on standard finite elements on the one hand and on structure-preserving geometric finite elements on the other hand. We tested and compared the schemes in the linear and in the nonlinear stage. We show that the structure-preserving algorithm leads to better results in both stages. This can be related to the fact that the spatial discretization results in a large system of ordinary differential equations that exhibits a noncanonical Hamiltonian structure. To such systems special time integration schemes with good conservation properties can be applied.

Complexification and integrability in multidimensions

The complexification of the independent variables of nonlinear integrable evolution partial differential equations (PDEs) in two space dimensions, like the celebrated Kadomtsev-Petviashvili and Davey-Stewartson (DS) equations, yields nonlinear integrable equations in genuine 4 + 2, namely, in four real space dimensions (x1, x2, y1, y2) and two real time dimensions (t1, t2), as opposed to two complex space dimensions and one complex time dimension. The associated initial value problem for such equations, namely, the problem where the dependent variables are specified for all space variables at t1 = t2 = 0, can be solved via a non-local d-bar formalism. Here, the details of this formalism for the 4 + 2 DS system are presented. Furthermore, the linearised version of the 3 + 1 reduction of the 4 + 2 DS system is discussed. The construction of the nonlinear 3 + 1 reduction remains open, in spite of the fact that multi-soliton solutions for the 3 + 1 DS system already exist.

Mechanical topological insulator in zero dimensions

We study linear vibrational modes in finite isostatic Maxwell lattices, mechanical systems where the number of degrees of freedom matches the number of constraints. Recent progress in topological mechanics exploits the nontrivial topology of BDI class Hamiltonians in one dimenson and arising topological floppy modes at the edges. A finite frame, or zero-dimensional system, also exhibits a nonzero topological index according to the classification table. We construct mechanical insulating models in zero dimensions that complete the BDI classification in the available real space dimensions. We compute and interpret its nontrivial invariant ${\mathbb{Z}}_{2}$.

High-resolution three-dimensional structural microscopy by single-angle Bragg ptychography.

Coherent X-ray microscopy by phase retrieval of Bragg diffraction intensities enables lattice distortions within a crystal to be imaged at nanometre-scale spatial resolutions in three dimensions. While this capability can be used to resolve structure-property relationships at the nanoscale under working conditions, strict data measurement requirements can limit the application of current approaches. Here, we introduce an efficient method of imaging three-dimensional (3D) nanoscale lattice behaviour and strain fields in crystalline materials with a methodology that we call 3D Bragg projection ptychography (3DBPP). This method enables 3D image reconstruction of a crystal volume from a series of two-dimensional X-ray Bragg coherent intensity diffraction patterns measured at a single incident beam angle. Structural information about the sample is encoded along two reciprocal-space directions normal to the Bragg diffracted exit beam, and along the third dimension in real space by the scanning beam. We present our approach with an analytical derivation, a numerical demonstration, and an experimental reconstruction of lattice distortions in a component of a nanoelectronic prototype device.

Photonic gauge potential in a system with a synthetic frequency dimension.

We generalize the concept of photonic gauge potential in real space by introducing an additional "synthetic" frequency dimension in addition to the real space dimensions. As an illustration, we consider a one-dimensional array of ring resonators, each supporting a set of resonant modes having a frequency comb with spacing Ω, and undergoing a refractive index modulation at the modulation frequency equal to Ω. We show that the modulation phase provides a gauge potential in the synthetic two-dimensional space with the dimensions being the frequency and the spatial axes. Such a gauge potential can create a topologically protected one-way edge state in the synthetic space that is useful for high-efficiency generation of higher-order side bands.

Water Dynamics in Shewanella oneidensis at Ambient and High Pressure using Quasi-Elastic Neutron Scattering.

Quasielastic neutron scattering (QENS) is an ideal technique for studying water transport and relaxation dynamics at pico- to nanosecond timescales and at length scales relevant to cellular dimensions. Studies of high pressure dynamic effects in live organisms are needed to understand Earth’s deep biosphere and biotechnology applications. Here we applied QENS to study water transport in Shewanella oneidensis at ambient (0.1 MPa) and high (200 MPa) pressure using H/D isotopic contrast experiments for normal and perdeuterated bacteria and buffer solutions to distinguish intracellular and transmembrane processes. The results indicate that intracellular water dynamics are comparable with bulk diffusion rates in aqueous fluids at ambient conditions but a significant reduction occurs in high pressure mobility. We interpret this as due to enhanced interactions with macromolecules in the nanoconfined environment. Overall diffusion rates across the cell envelope also occur at similar rates but unexpected narrowing of the QENS signal appears between momentum transfer values Q = 0.7–1.1 Å−1 corresponding to real space dimensions of 6–9 Å. The relaxation time increase can be explained by correlated dynamics of molecules passing through Aquaporin water transport complexes located within the inner or outer membrane structures.

Effect of Coulomb collision on the negative ion extraction mechanism in negative ion sources.

To improve the H(-) ion beam optics, it is necessary to understand the energy relaxation process of surface produced H(-) ions in the extraction region of Cs seeded H(-) ion sources. Coulomb collisions of charged particles have been introduced to the 2D3V-PIC (two dimension in real space and three dimension in velocity space particle-in-cell) model for the H(-) extraction by using the binary collision model. Due to Coulomb collision, the lower energy part of the ion energy distribution function of H(-) ions has been greatly increased. The mean kinetic energy of the surface produced H(-) ions has been reduced to 0.65 eV from 1.5 eV. It has been suggested that the beam optics of the extracted H(-) ion beam is strongly affected by the energy relaxation process due to Coulomb collision.

Study of plasma meniscus and beam halo in negative ion sources using three dimension in real space and three dimension in velocity space particle in cell model

Our previous study by two dimension in real space and three dimension in velocity space-particle in cell model shows that the curvature of the plasma meniscus causes the beam halo in the negative ion sources. The negative ions extracted from the periphery of the meniscus are over-focused in the extractor due to the electrostatic lens effect, and consequently become the beam halo. The purpose of this study is to verify this mechanism with the full 3D model. It is shown that the above mechanism is essentially unchanged even in the 3D model, while the fraction of the beam halo is significantly reduced to 6%. This value reasonably agrees with the experimental result.

Virtuality in architecture: From perspective representation to augmented reality

Notion of virtuality correlates mainly to visual aspects of space, presuming that basic qualities of physical space can be simulated by graphics, providing not just visual illusion of the third dimension of real space, but psychological involvement and transfer of the spectator into the space of the picture, giving him the sense of the spatial location and presence. Creation of virtual space that could be perceptually sensed and by virtual presence modified and shaped, explored and experienced, is not just result of advanced computer technology, but could be traced through history of spatial representations, that was based mainly in artistic and architectural practice. Architecture, being leading field that synthesize representation, construction and sense of spatial creation, had to be involved in explorations of multidimensional complex network of dynamic informational space, that is revealed in its real and virtual dimension as unique universe. Real-time experience in virtual space allow access in the alternative dimension to every open mind, giving him possibilities to play and work, to construct and represent, search, explore and express, augmenting reality into the complex network of information flow between visible and invisible space.

Kinetic modeling of fast electron dynamics and self-consistent magnetic fields in a reversed field pinch

The dynamics of fast electrons in a reversed field pinch configuration is investigated by numerically solving the appropriate kinetic equation in three dimensions (two dimensions in velocity space and one dimension in real space). To this end, a Fokker–Planck code has been developed, including Coulomb collisions, direct current (dc) electric field, radial diffusion due to magnetic turbulence, ambipolar electric fields, and the self-consistent evaluation of the magnetic fields generated by the plasma itself. This has allowed the theoretical validation of the kinetic dynamo model in a realistic geometry. In contrast to fluid-turbulent theories, such a model predicts that the radial diffusion of fast electrons associated with stochastic magnetic fields might be able to sustain the reversed field configuration. Quantitatively, it is found that the level of magnetic turbulence necessary to obtain the toroidal field reversal at the plasma edge is compatible with levels typically measured in reversed field pinch devices. In particular, the main parameters of standard discharges in the largest existing facility of this type, RFX (reversed field experiment) [Proceedings of the 14th Conference on Plasma Physics and Controlled Nuclear Fusion Research, Würzburg, 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. 2, p. 583], have been successfully simulated.

Relativistic Shock Wave

Perpendicular shock waves in rather strong magnetic fields (ω ce ≥ω pe ) are studied by a 1- 2/2 dimension (one dimension in real space and three dimension in velocity space), fully relativistic, fully electromagnetic particle simulation with full ion and electron dynamics. In that parameter regime relativistic effects become important in fast magnetosonic shock waves, even if the thermal speeds of ions and electrons in the upstream region are much smaller than the speed of light; a shock wave can trap some ions and promptly accelerate them to relativistic energies. Furthermore, with the mechanism different from that of ions, some electrons also gain relativistic energies through interactions with strong electric fields in the shock region. By showing various simulation results, we discuss the acceleration proccsses in detail.

Three-Dimensional Imaging in Medicine: Holography

Two holographic methods for three-dimensional imaging in medicine are presented. The methods can be applied on the base of various primary projection methods, especially those of nuclear medicine and roentgenology. This three-dimensional display, which is not bound to complicated technical equipments such as computers and graphic displays, can be performed easily at any place: in conference rooms, in surgical units etc. It may be of particular importance for the surgeon in order to visualize the site directly and in its real space dimensions.