1D Theory Research Articles

Numerical studies on structure optimization and flow characteristics of a hydrogen recirculation ejector under multiple load conditions

Ejectors are ideal hydrogen recirculation devices for PEMFC systems but typically exhibit poor recirculation performance at low loads. For purpose of extending ejector's operating range in vehicular applications, the entraining performance across multiple loads should be focused. In this study, A 40 kW ejector was designed with a 1D theory and optimized using a 2D CFD model. Simulations were conducted to study the influence of various diameter and axial dimensions on the ejector's performance and flow characteristics. The results reveal that as the load increases from 20% to 100%, the suboptimal diffuser exit diameter decreases from 2.5 to 1.5 times the mixing chamber diameter, the optimal nozzle exit position increases from 0.59 to 0.63 times, and the optimal mixing chamber length increases from 2.2 to 4.3 times. A convergent nozzle with a short throat significantly improves low-load entraining performance and achieves the highest performance growth in the variable-nozzle design. Additionally, an optimization method for axial dimensions based on the proposed parameter flow uniformity was established, allowing for precise determination of the optimal dimensions through a few simulations.

Invariant regimes of Spencer scaling law for magnetic compression of rotating FRC plasma

Abstract The scaling laws for the magnetic compression of a toroidally rotating field reversed configuration (FRC) have been investigated in this work. The magnetohydrodynamics (MHD) simulations of the magnetic compression on rotating FRCs employing the NIMROD code (Sovinec et al 2004 J. Comput. Phys. 195 355), are compared with the Spencer’s one-dimensional (1D) theory (Spencer et al 1983 Phys. Fluids 26 1564) for a wide range of initial flow speeds and profiles. The toroidal flow can influence the scalings directly through the alteration of the compressional work as also evidenced in the 1D adiabatic model, and indirectly by reshaping the initial equilibrium. However, in comparison to the static initial FRC equilibrium cases, the pressure and the radius scalings remain invariant for the magnetic compression ratio B w 2 / B w 1 up to 6 in presence of the initial equilibrium flow, suggesting a broader applicable regime of the Spencer scaling law for FRC magnetic compression. The invariant scaling has been proven a natural consequence of the conservation of angular momentum of both fluid and magnetic field during the dynamic compression process.

What next: Further implosion space exploration on the path to NIF extended yield capability

We present quantitative motivations and assessments of various proposed and ongoing directions to further improving yields and target gain of igniting indirect-drive implosions at the National Ignition Facility (NIF). These include increasing compression and confinement time, improving hohlraum and ablator efficiency, and further increasing peak power and laser energy. 1D hydroscaled simulations, augmented by analytic 1D theory, have been used to project yield improvements for each of these implosion optimization tracks, normalized to the best current performing 4 MJ shot. At current NIF capabilities of 2.2 MJ, 450 TW, we project several paths could reach 15 MJ yield levels. We also expect several key implosion physics questions will be addressed in attempting to reach this yield level. These include demonstrating to what extent lower adiabat designs leading to higher compression will increase gain and efficiency, and whether we can reduce residual kinetic energy and ablator-fuel mix that is probably limiting the current burn-up fraction. For an envisaged NIF upgrade to EL = 3 MJ at fixed 450 TW peak power, scaling capsule size and fuel thicknesses faster than pure hydroscaling should allow for yields that could reach up to 60–80 MJ, depending on the efficiency gains realized in increasing deuterium-tritium fuel thickness, reducing hohlraum losses, and switching to lower Z ablators. The laser-plasma instability and beam transmission scaling in these larger hohlraums is shown to be favorable if the spot size is increased with hohlraum scale.

Permanent helical micro-undulators for x-ray free electron lasers

Helical Halbach undulators, formed by four alternately axially and radially magnetized rare-earth helices, produce a stronger field than two planar Halbach undulators with perpendicular polarization. Hybrid undulators of two longitudinally premagnetized rare-earth helices and two initially unmagnetized steel (or vanadium permendur) helices produce an equal or higher field and are easier to implement. We made sure that the required helices with a period of down to 3 mm or even less could be manufactured with high precision using Wire Electric Discharge Machining. According to the simulation results, when using identical electron bunches with moderate initial spreads in energy and angles, the gain in x-ray free electron laser (XFEL) power from replacing planar micro-undulators with the helical micro-undulators under consideration can be significantly greater than predicted by the simplest 1D theory with a cold electron beam. This makes such micro-undulators promising for creating compact XFELs of various types, both based on modern linear accelerators and plasma wakefield accelerators.

Entropy of flat space cosmologies from celestial dual

We construct a one-dimensional dual theory that effectively describes the sector of the (2+1)D flat gravity phase space near a flat space cosmology saddle labeled by definite mass and angular momentum. This Schwarzian-type action describes the dynamics of the (pseudo-)Goldstone bosons of BMS3 algebra on a circle as the symmetry is spontaneously and anomalously broken. This 1D theory, living on the celestial circle, provides the first explicit construction of a celestial dual theory in (2+1)D. We use it to calculate the semiclassical entropy of flat space cosmologies and find perfect agreement with existing literature. Published by the American Physical Society 2024

Realization of shorter substitutes for a percussive rock drill hammer by periodic redistribution of its mass and compliance

In percussive drilling of rock, use is made of high-amplitude short-duration force pulses generated through impacts of a hammer on a drill bit or a drill rod assembly. The mass of the hammer is crucial for the impact velocity and the impact frequency, while its length and variation of characteristic impedance control the duration and shape of the force pulses. High efficiency of conversion of kinetic impact energy to work results if the force pulses have suitable shapes and durations. Commonly, hammers of hydraulic rock drills are nearly uniform and generate nearly rectangular force pulses admitting high efficiencies. When space is constrained, short hammers are advantageous as they allow short rock drills. Here, therefore, shorter substitutes for uniform original hammers are sought. They should have the same mass as the original hammer, be shorter than the original hammer, and generate approximately the same impact force history as the original hammer. A method based on 1D theory is developed for realization of substitute hammers with axially periodic characteristic impedance. Impact force histories generated by such hammers agree well with that generated by a uniform original hammer in a 1D context, and also in a 3D context if 3D effects are small enough. Also, for bit-rock interaction conditions from soft to hard, the efficiencies obtained by use of substitute hammers agree well with that obtained by use of the original hammer.

One-dimensional viscoelastic von Kármán theories derived from nonlinear thin-walled beams

We derive an effective one-dimensional limit from a three-dimensional Kelvin–Voigt model for viscoelastic thin-walled beams, in which the elastic and the viscous stress tensor comply with a frame-indifference principle. The limiting system of equations comprises stretching, bending, and twisting both in the elastic and the viscous stress. It coincides with the model already identified via Friedrich and Kružík (Arch Ration Mech Anal 238:489–540, 2020) and Friedrich and Machill (Nonlinear Differ Equ Appl NoDEA 29, Article number: 11, 2022) by a successive dimension reduction, first from 3D to a 2D theory for von Kármán plates and then from 2D to a 1D theory for ribbons. In the present paper, we complement the previous analysis by showing that the limit can also be obtained by sending the height and width of the beam to zero simultaneously. Our arguments rely on the static Gamma -convergence in Freddi et al. (Math Models Methods Appl Sci 23:743–775, 2013), on the abstract theory of metric gradient flows (Ambrosio et al. in Gradient flows in metric spaces and in the space of probability measures. Lectures mathematics, ETH Zürich, Birkhäuser, Basel, 2005), and on evolutionary Gamma -convergence (Sandier and Serfaty in Commun Pure Appl Math 57:1627–1672, 2004).

Liquid Permeability Determination from Vacuum Imbibition in Tight/Shale Core Plugs

Liquid permeability is a key petrophysical parameter that quantifies the ability of a liquid to flow through porous rock/soil and can be used in determining the efficiency of many subsurface processes, including enhanced hydrocarbon recovery, groundwater transport, carbon dioxide geostorage, underground hydrogen storage, etc. However, it is time-consuming (usually >16–240 h) and challenging to measure the liquid permeability for tight/shale rocks, particularly when the permeability is 100 nD or lower. The objective of this study is to develop a rapid and simple approach to determine liquid (brine or oil) permeability in tight siltstones/shales. Specifically, the developed method is based on the combination of one-dimensional (1D) vacuum imbibition experiments in tight/shale core plugs and a modified Lucas–Washburn model. For our proof-of-concept study, the results have demonstrated that (1) only 44–116 h are required to determine the liquid permeability (98–608 nD) for the analyzed samples from the Montney and Yanchang Formations; and (2) the acquired brine permeability was 28.3–28.5% lower than the slip-corrected nitrogen (N2) permeability derived from the pulse-decay permeability tests. This is the first attempt to determine the absolute permeability of a liquid according to a 1D vacuum imbibition experiment and theory. This study provides a promising technique for the fast characterization of ultratight formation permeability of around 100 nD.

Achieving one-dimensionality with attractive fermions

In this article we discuss the accuracy of effective one-dimensional (1D) theories used to describe the behavior of ultracold atomic ensembles confined in quantum wires by a harmonic trap. We derive, within a fully many-body approach, the effective Hamiltonian describing this class of systems and we calculate the beyond-mean-field corrections to the energy of the ground state arising from virtual transitions towards the excited state of the confining potential. We find that, due to the Pauli principle, effective finite-range corrections are one order of magnitude larger than effective three-body interactions. By comparing to exact solutions of the purely 1D problem, we conclude that a 1D effective theory provides a good description of the ground state of the system for a rather large range of interaction parameters.

Probing the Degree of Coherence through the Full 1D to 3D Crossover.

We experimentally study a gas of quantum degenerate ^{87}Rb atoms throughout the full dimensional crossover, from a one-dimensional (1D) system exhibiting phase fluctuations consistent with 1D theory to a three-dimensional (3D) phase-coherent system, thereby smoothly interpolating between these distinct, well-understood regimes. Using a hybrid trapping architecture combining an atom chip with a printed circuit board, we continuously adjust the system's dimensionality over a wide range while measuring the phase fluctuations through the power spectrum of density ripples in time-of-flight expansion. Our measurements confirm that the chemical potential μ controls the departure of the system from 3D and that the fluctuations are dependent on both μ and the temperature T. Through a rigorous study we quantitatively observe how inside the crossover the dependence on T gradually disappears as the system becomes 3D. Throughout the entire crossover the fluctuations are shown to be determined by the relative occupation of 1D axial collective excitations.

MHD simulation on magnetic compression of field reversed configurations with NIMROD

Magnetic compression has long been proposed a promising method for plasma heating in a field reversed configuration (FRC). However, it remains a challenge to fully understand the physical mechanisms underlying the compression process, due to its highly dynamic nature beyond the one-dimensional (1D) adiabatic theory model (Spencer et al 1983 Phys. Fluids 26 1564). In this work, magnetohydrodynamics simulations on the magnetic compression of FRCs using the NIMROD code (Sovinec et al 2004 J. Comput. Phys. 195 355) and their comparisons with the 1D theory have been performed. The effects of the assumptions of the theory on the compression process have been explored, and the detailed profiles of the FRC during compression have been investigated. The pressure evolution agrees with the theoretical prediction under various initial conditions. The axial contraction of the FRC can be affected by the initial density profile and the ramping rate of the compression magnetic field, but the theoretical predictions on the FRC’s length in general and the relation in particular hold approximately well during the whole compression process, where r s is the major radius of FRC separatrix and r o is that of the magnetic axis. The evolutions of the density and temperature can be affected significantly by the initial equilibrium profile and the ramping rate of the compression magnetic field. During the compression, the major radius of the FRC is another parameter that is susceptible to the ramping rate of the compression field. Basically, for the same magnetic compression ratio, the peak density is higher and the FRC’s radius r s is smaller than the theoretical predictions.

Coupling between Abyssal Boundary Layers and the Interior Ocean in the Absence of Along-Slope Variations

Abstract To close the overturning circulation, dense bottom water must upwell via turbulent mixing. Recent studies have identified thin bottom boundary layers (BLs) as locations of intense upwelling, yet it remains unclear how they interact with and shape the large-scale circulation of the abyssal ocean. The current understanding of this BL–interior coupling is shaped by 1D theory, suggesting that variations in locally produced BL transport generate exchange with the interior and thus a global circulation. Until now, however, this picture has been based on a 1D theory that fails to capture the local evolution in even highly idealized 2D geometries. The present work applies BL theory to revised 1D dynamics, which more naturally generalizes to two and three dimensions. The BL is assumed to be in quasi-equilibrium between the upwelling of dense water and the convergence of downward buoyancy fluxes. The BL transport, for which explicit formulas are presented, exerts an influence on the interior by modifying the bottom boundary condition. In 1D, this BL transport is independent of the interior evolution, but in 2D the BL and interior are fully coupled. Once interior variables and the bottom slope are allowed to vary in the horizontal, the resulting convergences and divergences in the BL transport exchange mass with the interior. This framework allows for the analysis of previously inaccessible problems such as the BL–interior coupling in the presence of an exponential interior stratification, laying the foundation for developing a full theory for the abyssal circulation.

Cylinder quantum field theories at small coupling

We show that any 2D scalar field theory compactified on a cylinder and with a Fourier expandable potential V is equivalent, in the small coupling limit, to a 1D theory involving a massless particle in a potential V and an infinite tower of free massive Kaluza-Klein (KK) modes. Moving slightly away from the deep IR region has the effect of switching on interactions between the zero mode and the KK modes, whose strength is controlled by powers of the coupling, hence making the interactions increasingly suppressed. We take the notable example of Liouville field theory and, starting from its worldline version, we compute the torus (one-loop) partition function perturbatively in the coupling constant. The partition function at leading order is invariant under a T-duality transformation that maps the radius of the cylinder to its inverse and rescales it by the square of the Schwinger parameter of the cylinder. We show that this behavior is a universal feature of cylinder QFTs.

One‐Step Leapfrog Locally 1D Theory with Higher‐Order Enhanced Absorption for Fine‐Details Simulation

AbstractBased on a higher‐order concept and one‐step leapfrog formulation, an unconditionally stable leapfrog locally 1D (LOD) perfectly matched layer (PML) is proposed to not only enhance the absorbing performance in terminating an unbounded finite‐difference time‐domain (FDTD) algorithm but also improve the computational efficiency compared with the LOD‐FDTD algorithm. Most precisely, the PML is implemented by the auxiliary differential equations method. By applying the proposed scheme to a 3D electromagnetics simulation, the proposal can utilize the unconditionally stable algorithm, one‐step leapfrog formulation, and higher‐order concept in terms of attenuating low‐frequency propagation waves, enhancing the performance, and improving the computational efficiency. Numerical examples including the magic‐T waveguide model, very large‐scale integration circuits, and the structure of metamaterials are investigated to further demonstrate the efficiency, performance, and unconditional stability. The results help conclude that the proposed scheme can attain better performance and efficiency when the time step far surpasses the Courant–Friedrichs–Lewy limit. Most importantly, by employing the one‐step leapfrog formulation in the LOD algorithm, the memory requirements and simulation duration can be reduced significantly, indicating the improvement of the algorithm compared with the published LOD schemes.

Application of an extended two-dimensional inverse method in turbine volute design

Nozzleless housings for turbocharger turbines accelerate and guide flow into downstream rotors. Their design affects the aerodynamic performance and reliability of the turbines. Due to the three-dimensional nature of the volute of the housings, turbine housing volute design is largely based on extended 1D theories and trial-and-error method. In this paper, a detailed description of an extended two-dimensional theory for volute design is given, including its numerical implementation. The method is then applied to design a twin-entry turbine housing for a turbocharger turbine under both equal and unequal admissions, to replace a highly optimized, manually designed housing. The results show that the new volute achieves the same turbine aerodynamic performance as the manually optimized volute with greatly reduced design time, and it also generates more uniform rotor inlet condition with lower pressure excitation force. A breakdown of the stage loss shows that the loss in the new volute housing is larger than that in the manual housing due to its smaller overall dimensions, but the losses inside rotor and downstream diffuser are both reduced due to the more uniform volute exit flow. A discussion on the secondary flow in the two volutes is carried out to show how the volute geometry, through influencing the radial discharge from the volute exit, affects this flow. A further discussion on the flow angle jump around the tongue is placed at the end of the paper to show the mechanism of this jump, how to control it in volute design, and to offer a way forward to improve the volute design method.

One-dimensional sectors from the squashed three-sphere

Three-dimensional mathcal{N} = 4 superconformal field theories contain 1d topological sectors consisting of twisted linear combinations of half-BPS local operators that can be inserted anywhere along a line. After a conformal mapping to a round three-sphere, the 1d sectors are now defined on a great circle of S3. We show that the 1d topological sectors are preserved under the squashing of the sphere. For gauge theories with matter hypermultiplets, we use supersymmetric localization to derive an explicit description of the topological sector associated with the Higgs branch. Furthermore, we find that the dependence of the 1d correlation functions on the squashing parameter b can be removed after appropriate rescalings. One can introduce real mass and Fayet-Iliopolous parameters that, after appropriate rescalings, modify the 1d theory on the squashed sphere precisely as they do on the round sphere. In addition, we also show that when a generic 3d mathcal{N} = 4 theory is deformed by real mass parameters, this deformation translates into a universal deformation of the corresponding 1d theory.

Infinite-dimensional algebraic mathfrak{Spin} (N) structure in extended/higher dimensional SUSY holoraumy for valise and on shell supermultiplet representations

We explore the relationship between holoraumy and Hodge duality beyond four dimensions. We find this relationship to be ephemeral beyond six dimensions: it is not demanded by the structure of such supersymmetrical theories. In four dimensions for the case of the vector-tensor mathcal{N} = 4 multiplet, however, we show that such a linkage is present. Reduction to 1D theories presents evidence for a linkage from higher-dimensional supersymmetry to an infinite-dimensional algebra extending mathfrak{Spin} (N).

Energy efficiency of detonation combustion in supersonic ramjet engines

The energy efficiency of a supersonic ramjet engine with detonation combustion of a hydrogen-air mixture in an axisymmetric Laval nozzle is considered. First of all, within the framework of the one-dimensional (1D) theory, it is shown that extreme combustion corresponding to the Chapman-Jouguet (C.-J.) deflagration, like constant pressure combustion, surpasses detonation in energy efficiency. However, this advantage becomes insignificant with an increasing the free-flow Mach number. Based on the results of the 1D theory, an axisymmetric Laval nozzle is constructed, which provides steady-state detonation combustion of a stoichiometric hydrogen-air mixture at an altitude of about 40 km and with freestream Mach numbers 9 and 12. The efficiency of detonation combustion in this case is about 35% instead of the maximum 65% according to the 1D theory.

General scaling laws of space charge effects in field emission

The characteristics of field electron and ion emission change when the space charge formed by the emitted charge is sufficient to suppress the extracting electric field. This phenomenon is well described for planar emitting diodes by the one dimensional (1D) theory. Here we generalize for any 3D geometry by deriving the scaling laws describing the field suppression in the weak space charge regime. We propose a novel corrected equivalent planar diode model, which describes the space charge effects for any geometry in terms of the 1D theory, utilizing a correction factor that adjusts the diode’s scaling characteristics. We then develop a computational method, based on the particle-in-cell (PIC) technique, which solves numerically the space charge problem. We validate our theory by comparing it to both our numerical calculations and existing experimental data, either of which can be used to obtain the geometrical correction factor of the corrected equivalent planar diode model.

Anomalous Dynamics of QBO Disruptions Explained by 1D Theory with External Triggering

AbstractThe quasi-biennial oscillation (QBO) is an alternating, descending pattern of zonal winds in the tropical stratosphere with a period averaging 28 months. The QBO was disrupted in 2016, and arguably again in 2020, by the formation of an anomalous easterly shear zone, and unprecedented stagnation and ascent of shear zones aloft. Several mechanisms have been implicated in causing the 2016 disruption, most notably triggering by horizontal eddy momentum flux divergence, but also anomalous upwelling and wave stress. In this paper, the 1D theory of the QBO is used to show how seemingly disparate features of disruptions follow directly from the dynamics of the QBO response to triggering. The perturbed QBO is interpreted using a heuristic version of the 1D model, which establishes that 1) stagnation of shear zones aloft resulted from wave dissipation in the shear zone formed by the triggering, and 2) ascent of shear zones aloft resulted from climatological upwelling advecting the stagnant shear zones. Obstacles remain in the theory of triggering. In the 1D theory, the phasing of the triggering is key to determining the response, but the dependence on magnitude is less steep. Yet in MERRA-2, there are triggering events only 20% weaker than the 2016 triggering and equal to the 2020 triggering that did not lead to disruptions. Complicating matters further, MERRA-2 has record-large analysis tendencies during the 2016 disruption, reducing confidence in the resolved momentum budget.