Time-dependent Geometry Research Articles

Time-dependent Hamiltonians and geometry of operators generated by them.

We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we calculate the bi-invariant cost associated with these time-dependent Hamiltonians by suitably regularizing their norms and obtain analytical expressions of the costs for several well-known time-dependent quantum mechanical systems. In particular, we show that an equivalence exists between the total costs of obtaining an operator through time evolution generated by a unit mass harmonic oscillator whose frequency depends on time, and a harmonic oscillator whose both mass and frequency are functions of time. These results are illustrated with several examples, including a specific smooth quench protocol where the comparison of time variation of the cost with other information theoretic quantities, such as the Shannon entropy, is discussed.

Time-dependent probability density functions and information geometry in a stochastic prey–predator model of fusion plasmas

Time-dependent probability density functions and information geometry in a stochastic prey–predator model of fusion plasmas

Control of waves on Lorentzian manifolds with curvature bounds

We prove boundary controllability results for wave equations (with lower-order terms) on Lorentzian manifolds with time-dependent geometry satisfying suitable curvature bounds. The main ingredient is a novel global Carleman estimate on Lorentzian manifolds that is supported in the exterior of a null (or characteristic) cone, which leads to both an observability inequality and bounds for the corresponding constant. The Carleman estimate also yields a unique continuation result on the null cone exterior, which has applications toward inverse problems for linear waves on Lorentzian backgrounds.

Local spherical collapsing box in Athena++ : Numerical implementation and benchmark tests

We implement a local model for a spherical collapsing or expanding gas cloud in the Athena++ magnetohydrodynamic code. This local model consists of a Cartesian periodic box with time-dependent geometry. We present a series of benchmark test problems, including nonlinear solutions and linear perturbations of the local model, confirming the code's desired performance. During a spherical collapse, a horizontal shear flow is amplified, corresponding to angular momentum conservation of zonal flows in the global problem; wave speed and the amplitude of sound waves increase in the local frame, due to the reduction in the characteristic length scale of the box, which can lead to an anisotropic effective sound speed in the local box. Our code conserves both mass and momentum-to-machine precision. This numerical implementation of the local model has potential applications to the study of local physics and hydrodynamic instabilities during protostellar collapse, providing a powerful framework for better understanding the earliest stages of star and planet formation.

Prediction of electronic density of states in guanine-TiO2 adsorption model based on machine learning

Prediction of electronic density of states in guanine-TiO2 adsorption model based on machine learning

Page curve of AdS-Vaidya model for evaporating black holes

We study an evaporating black hole in the boundary conformal field theory (BCFT) model under the fully time-dependent AdS-Vaidya spacetime geometry. We introduce the time-dependent finite bath termed the effective Hawking radiation region. This is described by a nontrivial BCFT solution that acts as a time-dependent brane which we call the moving end-of-the-radiation (METR) brane that leads to a new type of Hubeny-Rangamani-Takayanagi surface. We further examine the island formulation in this particular time-dependent spacetime. The Page curve is calculated by using Holographic Entanglement Entropy (HEE) in the context of double holography.

Statistical analysis of magnetic divertor configuration influence on H-mode transitions

DIII-D plasmas are compared for two upper divertor configurations: with the outer strike point on the small angle slot (SAS) divertor target and with the outer strike point on the horizontal divertor target (HT). Scanning the vertical distance between the magnetic null point and the divertor target over a range 0.10–0.16 m is shown to increase the threshold power, Pth , and edge plasma power, PLoss , for the low-to-high confinement (L–H) and H–L transitions respectively, by up to a factor of 1.4. The X-point height scans were performed at three L-mode core plasma line average electron densities, n¯e= 1.2, 2.2 and 3.6 ×1019m−3 , to investigate the density dependence of divertor magnetic configuration influence on Pth . The X-point height, Zx-pt , was further extended across the range 0.16–0.22 m with the more open HT divertor configuration, for which a clear decrease in Pth with increasing Zx-pt is observed. The dependence of Pth on divertor magnetic geometry is further investigated using a time-dependent probability density function (PDF) model and information geometry to elucidate the roles played by pedestal plasma turbulence and perpendicular velocity flows. The degree of stochasticity of the plasma turbulence is observed to be sensitive to the plasma heating rate. The calculated square of the information rate shows changes in the relative density fluctuations and perpendicular velocity PDFs begin 2–5 ms prior to the L–H transition for three plasmas; providing a crucial measurement of the dynamic timescale of external transport barrier formation. Additionally, both information length and rate provide potential predictors of the L–H transition for these plasmas.

Hybrid Schrödinger-Ginzburg-Landau (Sch-GL) approach to study of superconducting integrated structures

Hybrid Schrödinger-Ginzburg-Landau approach is based on the fact of the mathematical similarity of Ginzburg-Landau (GL) and Schrödinger formalisms. Starting from Schrödinger approach by replacing the term V (x)−E with the term α(x)+β(x)|ψ(x)|2 we get the Ginzburg-Landau equation. In the proposed relaxation algorithm, we use one- and two-dimensional ground energy solutions of the Schrödinger equation and apply them as a starting trial solution for the GL relaxation method. The obtained numerical results and used methodology form the basis of the simulation platform for studying superconducting integrated structures and modeling various superconducting devices, including their time-dependent geometry.

Time-dependent probability density functions, information geometry and entropy production in a stochastic prey–predator model of fusion plasmas

A stochastic, prey–predator model of the L–H transition in fusion plasma is investigated. The model concerns the regulation of turbulence by zonal and mean flow shear. Independent delta-correlated Gaussian stochastic noises are used to construct Langevin equations for the amplitudes of turbulence and zonal flow shear. We then find numerical solutions of the equivalent Fokker–Planck equation for the time-dependent joint probability distribution of these quantities. We extend the earlier studies [Kim and Hollerbach, Phys. Rev. Res. 2, 023077 (2020) and Hollerbach et al., Phys. Plasmas 27, 102301 (2020)] by applying different functional forms of the time-dependent external heating (input power), which is increased and then decreased in a symmetric fashion to study hysteresis. The hysteresis is examined through the probability distribution and statistical measures, which include information geometry and entropy. We find strongly non-Gaussian probability distributions with bi-modality being a persistent feature across the input powers; the information length to be a better indicator of distance to equilibrium than the total entropy. Both dithering transitions and direct L-–H transitions are (also) seen when the input power is stepped in time. By increasing the number of steps, we see less hysteresis (in the statistical measures) and a reduced probability of H-mode access; intermittent zonal flow shear is seen to have a role in the initial suppression of turbulence by zonal flow shear and stronger excitation of intermittent zonal flow shear for a faster changing input power.

EFFICIENT SPATIO-TEMPORAL MODELLING TO ENABLE TOPOLOGICAL ANALYSIS

Abstract. Time-dependent analysis scenarios such as heat, wind or flood analysis in cities and in landscapes need a correct and consistent modelling of geometry and topology over time. However, hitherto efficient time-dependent geometry models and topological analysis based on a mathematically sound theory were neglected when modelling objects in the built and natural environment. This is surprising as incorrect topological relationships over time such as not fitting neighbourhoods of surfaces or solids inevitably lead to wrong analysis results. In this paper we propose the combination of a spatio-temporal geometry model together with a topological schema to provide accessible and consistent objects over time. Where an efficient spatio-temporal geometry model reduces redundant geometric data and enables spatio-temporal queries, an efficient topological model minimizes the number of relations as far as possible and enables robust topological queries. The geometry model uses the concepts of point tubes, delta storage as well as net components and pre- and post-objects to enable the change of geometry and topology over time for natural structures, e.g., digital terrain models (DTM). Geometry here are the boundary and interior coordinates of the objects whereas topology here is interpreted in a wider sense than only focusing on geometrically induced topology to maintain topological consistency by the management of incidence relations. In addition, the topological schema introduces three basic bidirectional relation types to manage aggregations, abstractions and incidences in order to provide a general abstract topological schema for the management of complex intra- and inter-related spatio-temporal objects to enable the modelling of consistent complex topology over time. Finally, a conclusion is given highlighting the applicability of the approach and future research.

Numerical investigation of effects of tongue articulation and velopharyngeal closure on the production of sibilant [s

A numerical simulation of sibilant /s/ production with the realistically moving vocal tract was conducted to investigate the flow and acoustic characteristics during the articulation process of velopharyngeal closure and tongue movement. The articulation process was simulated from the end of /u/ to the middle of /s/ in the Japanese word /usui/, including the tongue elevation and the velopharyngeal valve closure. The time-dependent vocal tract geometry was reconstructed from the computed tomography scan. The moving immersed boundary method with the hierarchical structure grid was adopted to approach the complex geometry of the human speech organs. The acoustic characteristics during the co-articulation process were observed and consistent with the acoustic measurement for the subject of the scan. The further simulations with the different closing speeds of the velopharyngeal closure showed that the far-field sound during the co-articulation process was amplified with the slower closing case, and the velum closure speed was inverse proportional to the sound amplitude with the slope value of − 35.3 dB s/m. This indicates possible phonation of indistinguishable aeroacoustics sound between /u/ and /s/ with slower velopharyngeal closure.

Modelling and simulations of reactor neutron noise induced by mechanical vibrations

Modelling and simulations of reactor neutron noise induced by mechanical vibrations

Scalar quantum fields in cosmologies with2+1spacetime dimensions

Motivated by the possibility to use Bose-Einstein condensates as quantum simulators for spacetime curvature, we study a massless relativistic scalar quantum field in spatially curved Friedmann-Lema\^itre-Robertson-Walker universes with $d=2+1$ spacetime dimensions. In particular, we investigate particle production caused by a time-dependent background geometry, by means of the spectrum of fluctuations and several two-point field correlation functions. We derive new analytical results for several expansion scenarios.

Dynamic behaviors of anisodiametric bubbles under effects of horizontal attraction and vertical wake

The present study aims to describe the interaction between rising bubbles of different sizes. Coaxial and triangle bubble configurations were investigated. Bubble sizes ranged from 4.0 mm to 10.0 mm. Three-dimensional unsteady numerical simulations were performed and the volume of fluid multiphase model was employed. The numerical scheme was validated through experimental results. Time-dependent bubble geometry, bubble velocity, and near-bubble flow patterns were obtained. The results show that the participation of lateral bubbles causes coalescence delay. The mergence of bubbles is followed by an immediate decrease in bubble velocity. Liquid flow structures tend to be combined accordingly as the bubbles coalesce. For the triangle configuration, the first coalescence of small bubbles takes place between the trailing bubbles. As bubble size increases, the first coalescence arises between the leading bubble and the left trailing bubble.

Multi-instrument Bayesian reconstruction of plasma shape evolution in the C-2W experiment

We determined the time-dependent geometry, including high-frequency oscillations, of the plasma density in TAE's C-2W experiment [Gota et al., Nucl. Fusion 59, 112009 (2019)]. This was done as a joint Bayesian reconstruction from a 14-chord FIR interferometer in the midplane, 32 Mirnov probes at the periphery, and 8 shine-through detectors at the targets of the neutral beams. For each point in time, we recovered, with credibility intervals, the radial density profile of the plasma; bulk plasma displacement; and amplitudes, frequencies, and phases of the azimuthal modes n = 1, …, 4. Also reconstructed were the radial profiles of the deformations associated with each of the azimuthal modes. Bayesian posterior sampling was done via Hamiltonian Monte Carlo with custom preconditioning. This gave us a comprehensive uncertainty quantification of the reconstructed values, including correlations and some understanding of multimodal posteriors.

A cut finite element method for non-Newtonian free surface flows in 2D - application to glacier modelling

In ice sheet and glacier modelling, the Finite Element Method is rapidly gaining popularity. However, constructing and updating meshes for ice sheets and glaciers is a non-trivial and computationally demanding task due to their thin, irregular, and time dependent geometry. In this paper we introduce a novel approach to ice dynamics computations based on the unfitted Finite Element Method CutFEM, which lets the domain boundary cut through elements. By employing CutFEM, complex meshing and remeshing is avoided as the glacier can be immersed in a simple background mesh without loss of accuracy. The ice is modelled as a non-Newtonian, shear-thinning fluid obeying the p-Stokes (full Stokes) equations with the ice atmosphere interface as a moving free surface. A Navier slip boundary condition applies at the glacier base allowing both bedrock and subglacial lakes to be represented. Within the CutFEM framework we develop a strategy for handling non-linear viscosities and thin domains and show how glacier deformation can be modelled using a level set function. In numerical experiments we show that the expected order of accuracy is achieved and that the method is robust with respect to penalty parameters. As an application we compute the velocity field of the Swiss mountain glacier Haut Glacier d'Arolla in 2D with and without an underlying subglacial lake, and simulate the glacier deformation from year 1930 to 1932, with and without surface accumulation and basal melt.

Pore pressure evaluation of formation testing while drilling under supercharged conditions

Pore pressure evaluation of formation testing while drilling under supercharged conditions

Holographic approach to thermalization in general anisotropic theories

We employ the holographic approach to study the thermalization in the quenched strongly-coupled field theories with very general anisotropic scalings including Lifshitz and hyperscaling violating fixed points. The holographic dual is a Vaidya-like time-dependent geometry where the asymptotic metric has general anisotropic scaling isometries. We find the Ryu-Takanayagi extremal surface and use it to calculate the time-dependent entanglement entropy between a strip region with width 2R and its outside region. In the special case with an isotropic metric, we also explore the entanglement entropy for a spherical region of radius R. The growth of the entanglement entropy characterizes the thermalization rate after a quench. We study the thermalization process in the early times and late times in both large R and small R limits. The allowed scaling parameter regions are constrained by the null energy conditions as well as the condition for the existence of the Ryu-Takanayagi extremal surfaces. This generalizes the previous works on this subject. All obtained results can be compared with experiments and other methods of probing thermalization.

Micropart Motion on a Surface Due to Controlled Surface Excitation

Many types of devices and handling platforms are used for microscale manipulation and microassembly ranging from microgrippers for individual part handling to work surfaces equipped with discrete actuators capable of simultaneous multiple part handling and manipulation. Micropart handling using discrete actuators suffers from dead zone constraint that requires the size of the part to be larger than the gap between consecutive actuators to ensure part contact with multiple actuators at all times for proper handling. In the context of the dead zone constraint, a new micromanipulation technique was proposed in our previous work based on the concept of active deformable surface. The time-dependent deformation geometry of the micropart carrying surface is controlled by actuators rigidly attached to it. The deformation acceleration imparted by the actuators generates an inertia which, considering other parameters, can induce a motion on the micropart placed on the surface. These parameters include size, mass and material properties of the micropart and the surface roughness characteristics. This research extends our previous work of modeling micropart dynamics and motion from 1D to motion on a 2D surface. The mathematical model is developed and subsequently employed in numerical simulations to study the micropart motion and controlled translocation on the deformable active surface. The analysis allows for the identification of a feasible region of influence of the actuator, effects of surface motion characteristics, micropart convergence at particular locations and evaluation of motion characteristics. The results of this research could be advantageously employed for the development of 2D microconveyors as an integral component of microassembly platforms.

Accelerator Grid Life Modeling of T6 Ion Thruster for BepiColombo

The T6 ion thruster is providing in-space propulsion for the BepiColombo mission, currently en route to Mercury. Simulations of the accelerator grid erosion during flight operation were carried out using the CEX2D and CEX3D codes in order to verify that the grid lifetime will be sufficient to impart the 5.75 total impulse per thruster required for the mission. Before calculating in-space erosion rates, the models were benchmarked against data from long-duration wear tests. Two-dimensional simulations tracked the time-dependent grid geometry and calculated changes in the electron backstreaming limit as the grids eroded. Sensitivity studies assessed the impact of uncertainty in the operating screen-to-accelerator grid gap on . Three-dimensional simulations employed a particle-in-cell model for the charge exchange ions and were able to accurately reproduce the nonaxisymmetric pits and grooves erosion pattern observed on the downstream face of the accelerator grid following ground testing. Charge exchange ion space charge effects were found to broaden the pit erosion features in flight, further reducing the peak erosion rate relative to that observed on the ground. The simulations predicted that T6 will have sufficient margin against both electron backstreaming and accelerator grid wearthrough over the duration of the mission.