Zeroth Order Research Articles

Hydrogen desorption kinetics of hafnium hydride powders

The kinetics of hydrogen gas release from hafnium hydride are investigated by combining experiments and density functional theory. The material is a candidate neutron moderator and attenuator for compact nuclear reactors, where hydrogen release will lead to a degradation in moderating function. Experimentally, we have studied the decomposition of epsilon phase (HfH2-x) powders from 25-1000°C using thermogravimetry and X-ray diffraction. Isochronal heating reveals 3 characteristic desorption regions corresponding to the release of hydrogen from each phase (ε-HfH2-x, δ-HfH1.6-x and α-Hf), at ∼ 350, 415, and 700°C. These results are well supported by the modelling output from density functional theory. A Kissinger analysis allowed for activation energies for desorption to be calculated (∼150 kJ/mol, 170 kJ/mol and 90 kJ/mol respectively). The peak shape and desorption rate data suggests that a second order diffusion limited reaction controls the ε→ε+δ desorption, a first order interface limited reaction controls the ε+δ→δ reaction, and a surface limited zeroth order reaction limits the complete desorption of the δ+α phase. The analysis suggests that, at least for δ→α regime, engineering solutions for improved thermal stability should focus on reductions in surface reactivity.

Scattering-Free and Fast Response Polymer Brush-Stabilized Liquid Crystals Beam Steering Using Surface-Initiated Polymerization Technique.

Nonmechanical fast response optical beam steering technology is increasingly essential for telecommunications, imaging systems, optical sensing, displays, and military applications. Polymer network liquid crystal (PNLC) beam steering can achieve submillisecond response times but faces limitations due to scattering issues arising from the refractive index mismatch between the polymer network and the liquid crystals (LCs). In this article, we demonstrate a scattering-free, fast-response LC beam steering by using polymer brushes to stabilize the gradient refractive index. First, the initiator is incorporated into the alignment layer and the monomer is mixed into the LC layer. Surface-initiated polymerization (SIP) is then employed to grow the polymer brushes exclusively on the substrate's surface, thus confining the polymer network's growth to the LC bulk and reducing interfacial scattering. For polymer brush stabilized liquid crystal (PBSLC) beam steering device with a period size of 225 μm and a cell gap of 7.2 μm, the average transmission rate reaches 88% in the visible light spectrum with a haze value of only 6.91. The steering angle is 0.16, and the diffraction efficiency is 80.3%. When a voltage of 35 Vrms is applied, the primary energy can be tuned to the zeroth order, with a response time close to 1 ms. By cascading two PBSLC beam steering devices with opposite steering directions, the primary energy of the beam can be adjusted between zeroth, +1, and -1 order. This method requires only a UV light source, a precision displacement stage, a power supply, and a mask, avoiding the need for expensive equipment and complex electrode fabrication. By adjustment of the phase change period, step width, and number of steps during fabrication, the steering angles and diffraction efficiency of the PBSLC beam steering device can be easily controlled, highlighting its significant potential for industrial production.

Stochastic zeroth order descent with structured directions

Stochastic zeroth order descent with structured directions

Guiding properties of Bessel–Gaussian and super-Gaussian pulses in inhomogeneous parabolic plasma channels

The guidance and stable propagation of laser pulses over many Rayleigh lengths are crucial for the plasma electron acceleration in the laser wakefield accelerators. Using plasma channels with specific characteristics can lead to the proper guidance of the laser pulse. Here, quasi-three-dimensional particle-in-cell (PIC) simulations are performed to investigate the guidance of Bessel–Gaussian pulse (BGP) of zeroth order and super-Gaussian pulse (SGP) of 3rd and 4th orders in an axially and radially inhomogeneous plasma channel. The effects of the channel radius and depth, the laser wavelength and initial spot size, and the plasma channel inhomogeneity on the guidance of the laser pulse are also examined. The results indicate that the guidance of a laser pulse in the plasma channel depends on the pulse profile, and under certain conditions, the pulses can be guided with the least variation of spot size in the inhomogeneous plasma channel. It is shown that the channel depth and the initial laser spot size are very effective in pulse guiding, as the values of these parameters increase, the pulse guidance is done better. In addition, the results show that the guidance of laser pulse is dependent on the type of plasma inhomogeneity represented by three different kinds of initial conditions, as considering the nonlinear-axial inhomogeneity in the parabolic plasma channel can lead to more convergence than the axially homogeneous and linear-axially plasma density profiles.

The motion of a self-propelling two-sphere swimmer in a weakly viscoelastic fluid

We study analytically the propulsion of a force- and torque-free swimmer composed of two counterrotating spheres of differing radii through a viscoelastic fluid described by the Giesekus constitutive model. Our analysis includes both swimmers composed of directly touching spheres and those composed of spheres separated by some finite distance. The propulsion speed of the swimmer is calculated by first expanding the equations of motion and the Giesekus constitutive model as a power series in the Weissenberg number, and then using the Lorentz reciprocal theorem to determine the first-order propulsion speed using the known flow fields for rotating and translating two-sphere geometries at zeroth order. We calculate the relative rotation speeds of the two spheres necessary to maintain the torque-free condition, including an approximate correction for fluid elasticity. The impact of the separation distance between the two spheres, the ratio of their radii, and the value of the Giesekus mobility parameter α on the propulsion speed are all examined; we find that the propulsion speed of the swimmer is maximized for two touching spheres with a radius ratio of approximately 0.7, with a Giesekus mobility parameter of α=0, corresponding to an Oldroyd-B fluid. We also quantify how the increased shear-thinning in the fluid, represented by increasing values of α, results in a significant decrease in the swimmer speed. Finally, through calculations of the fluid stresses around the two-sphere swimmer, we demonstrate the development of enhanced hoop stresses around the smaller sphere, which drive the expulsion of stretched fluid behind the smaller sphere and induce motion of the swimmer in the direction of the larger sphere.

Equivariant Divergence Formula for Hyperbolic Chaotic Flows

We prove the equivariant divergence formula for axiom A flow attractors. It is a pointwisely-defined and recursive formula for perturbation of SRB measures along center-unstable manifolds. It depends on only the zeroth and first order derivatives of the map, the observable, and the perturbation. Hence, the linear response acquires an ‘ergodic theorem’, which means that it can be sampled by recursively computing a few vectors on one orbit.

High-efficiency hard X-ray blazed diffraction via refraction by nanometer-scale prism arrays

X-ray transmission gratings are widely utilized as wavelength dispersion elements in inertial confinement fusion and X-ray astronomy fields due to their high tolerance for alignment errors, light weight and compact size. However, the high transmittance of the grating bars in the hard X-ray range can lead to reduced efficiency of all other diffraction orders except for straight through zeroth order. We propose a novel blazed refraction grating design for the hard X-ray range that combines the advantages of transmission gratings and compound refraction lenses for the first time, demonstrating its superior performance in high broadband efficiency through compound refraction and diffraction from nanometer-scale periodic arrays of silicon prisms using beam propagation method and Fraunhofer diffraction simulation. This research develops blaze methods in gratings design and provides a new solution for compact and sensitive spectrum measurement in hard X-ray range.

Optimal milling cutter helix selection for period doubling chatter suppression

In high speed milling, interrupted cutting conditions can lead to period doubling chatter vibrations. While many studies have already confirmed that the use of helical tools can effectively shrink or remove these regions of unstable cutting, none of them has provided clear guidance to select the minimum helix that completely cancels the period doubling lobes. This study addresses this gap by introducing a novel analytical formula for a critical tool helix pitch: if the helix pitch is below the critical flip depth of cut of the straight helix cutter multiplied by π, the flip lobes will totally vanish. This rule is not only valuable for chatter-free process planning purposes, but it also establishes exact limit below which the fast and simple zeroth order stability algorithm can provide exact stability boundaries for helical tools. The effectiveness of the formula is numerically corroborated over three different milling scenarios: thin wall milling, slender tool and machine tool structure chatter cases. Finally, the findings are validated through experimental cutting tests.

Purcell gain equalized zero-mode waveguide

We refresh the design of zero-mode waveguides (ZMWs) by introducing metamaterials that makes the zeroth order resonant mode existence. Of particular importance, the resulting electromagnetic field exhibits nearly constant distribution but not a trivial solution of Maxwell’s equation, showing great advantage to equalize the excitation rate of molecules throughout the waveguides. A closed form expression for the wave impedance is derived which is verified by the finite-difference time-domain simulations. Benefitted from the cavity Purcell effect which is lacking in existing ZMWs, fluorescence amplification and lifetime reduction are simultaneously enhanced. A practical design where the excitation volume reduced down to sub-zeptoliter and the fluorescence lifetime shortened to picosecond scale is illustrated. This result makes single molecule real time (SMRT) sensing of biochemical reactions at biophysically relevant concentrations (~ μM) possible, combining off-the-shelf ultrafast lasers.

General Condition for Polymer Cononsolvency in Binary Mixed Solvents.

Starting from a generic model based on the thermodynamics of mixing and abstracted from the chemistry and microscopic details of solution components, three consistent and complementary computational approaches are deployed to investigate the general condition for polymer cononsolvency in binary mixed solvents at the zeroth order. The study reveals χPS - χPC + χSC as the underlying universal parameter that regulates cononsolvency, where χαβ is the immiscibility parameter between the α- and β-component. Two disparate cononsolvency regimes are identified for χPS - χPC + χSC < 0 and χPS - χPC + χSC > 2, respectively, based on the behavior of the second osmotic virial coefficient at varying solvent mixture composition x C. The predicted condition is verified using self-consistent field calculations by directly examining the polymer conformational transition as a function of x C. It is further shown that in the regime χPS - χPC + χSC < 0, the reentrant polymer conformation transition is driven by maximizing the solvent-cosolvent contact, but in the regime χPS - χPC + χSC > 2, it is driven by promoting polymer and cosolvent contact. In-between the two regimes when neither effect is dominant, a monotonic response of polymer conformation to x C is observed. Effects of the mean-field approximation on the predicted condition are evaluated by comparing the mean-field calculations with computer simulations. It shows that the fluctuation effects lead to a higher threshold value of χPS - χPC + χSC in the second regime, where local enrichment of cosolvent in polymer proximity plays a critical role.

Comment on “ENN's roadmap for proton-boron fusion based on spherical torus” [Phys. Plasmas 31, 062507 (2024)

This comment discusses the feasibility of hot ion mode Ti/Te=4 for proton–boron fusion, which is critical for the roadmap proposed in Liu et al. [Phys. Plasmas 31, 062507 (2024)]. The hot ion mode Ti/Te=4 has been calculated to be far from accessible (Ti/Te&amp;lt;1.5 for Ti=150 keV) under the most optimal conditions if fusion provides the heating [Xie, Introduction to Fusion Ignition Principles: Zeroth Order Factors of Fusion Energy Research (USTC Press, Hefei, 2023)], i.e., that all fusion power serves to heat the ions and that electrons acquire energy only through interactions with ions. We also discuss if hot ion mode of Ti/Te=4 could be achieved by an ideal heating method, which is much more efficient than fusion itself (near 20 times fusion power for Ti=150 keV) and only heats the ions, whether it makes sense economically.

Controllable propagation of waveguide mode in multi-channel photonic crystal waveguide

In this paper, we introduce a new method to realize the separation of waveguide modes in photonic crystal waveguides by controlling the position and polarization of the dipole sources. Our study shows that the waveguide modes in the transversal channel and longitudinal channel can be manipulated, respectively, by the dipole sources placed within the corresponding channels. Based on this discovery, we may further adjust the dipole sources in the transversal (longitudinal) channel individually and separate the zeroth order and the first order modes to propagate towards the preassigned channels. Compared with the former schemes to realize the mode separation by changing the structure, our method is more intuitive, convenient, and flexible.

Can near-to-mid Infrared Spectral Energy Distribution Quantitatively Trace Protoplanetary Disk Evolution?

Infrared (IR) spectral energy distribution (SED) is the major tracer of protoplanetary disks. It was recently proposed to use the near-to-mid IR (or K-24) SED slope α defined between 2 and 24μm as a potential quantitative tracer of disk age. We critically examine the viability of this idea and confront it with additional statistics of IR luminosities and SED shapes. We point out that, because the statistical properties of most of the complicated physical factors involved in disk evolution are still poorly understood in a quantitative sense, the only viable way is to assume them to be random so that an idealized “average disk” can be defined, which allows the α histogram to trace its age. We confirm that the statistics of the zeroth order (luminosity), first order (slope α), and second order characteristics (concavity) of the observed K-24 SEDs indeed carry useful information upon the evolutionary processes of the “average disk”. We also stress that intrinsic diversities in K-24 SED shapes and luminosities are always large at the level of individual stars so that the application of the evolutionary path of the “average disk” to individual stars must be done with care. The data of most curves in plots are provided on GitHub (Disk-age package https://github.com/starage/disk-age/).

Reentrant phase transitions of quantum black holes

We show that backreaction of quantum fields on black hole geometries can trigger new thermal phase transitions. Specifically, we study the phase behavior of the three-dimensional quantum-corrected static Bañados-Teitelboim-Zanelli black hole, an exact solution to specific semiclassical gravitational equations due to quantum conformal matter, discovered through braneworld holography. Focusing on the canonical ensemble, for large backreaction, we find novel reentrant phase transitions as the temperature monotonically increases, namely, from thermal anti–de Sitter space to the black hole and back to thermal anti–de Sitter. The former phase transition is first-order, a quantum analog of the classical Hawking-Page phase transition, while the latter is zeroth order and has no classical counterpart. Published by the American Physical Society 2024

Pre-supernova evolution and final fate of stellar mergers and accretors of binary mass transfer

The majority of massive stars are expected to exchange mass or merge with a companion during their lives. This immediately implies that most supernovae (SNe) are from such post-mass-exchange objects. Here, we explore how mass accretion and merging affect the pre-SN structures of stars and their final fates. To this end, we modelled these complex processes by rapid mass accretion onto stars of different evolutionary stages and followed their evolution up to iron core collapse. We used the stellar evolution code MESA and inferred the outcome of core-collapse using a neutrino-driven SN model. Our models cover initial masses from 11 to 70 M⊙ and the accreted mass ranges from 10−200% of the initial mass. All models are non-rotating and for solar metallicity. The rapid accretion model offers a systematic way to approach the landscape of mass accretion and stellar mergers. It is naturally limited in scope and serves as a clean zeroth order baseline for these processes. We find that mass accretion, in particular onto post-main-sequence (post-MS) stars, can lead to a long-lived blue supergiant (BSG) phase during which stars burn helium in their cores. In comparison to genuine single stars, post-MS accretors have small core-to-total mass ratios, regardless of whether they end their lives as BSGs or cool supergiants (CSGs), and they can have genuinely different pre-SN core structures. As in single and binary-stripped stars, we find black-hole (BH) formation for the same characteristic CO core masses MCO of ≈7 M⊙ and ≳13 M⊙. In models with the largest mass accretion, the BH formation landscape as a function of MCO is shifted by about 0.5 M⊙ to lower masses, that is, such accretors are more difficult to explode. We find a tight relation between our neutron-star (NS) masses and the central entropy of the pre-SN models in all accretors and single stars, suggesting a universal relation that is independent of the evolutionary history of stars. Post-MS accretors explode both as BSGs and CSGs, and we show how to understand their pre-SN locations in the Hertzsprung-Russell (HR) diagram. Accretors exploding as CSGs can have much higher envelope masses than single stars. Some BSGs that avoid the luminous-blue-variable (LBV) regime in the HR diagram are predicted to collapse into BHs of up to 50 M⊙, while others explode in SNe and eject up to 40 M⊙, greatly exceeding ejecta masses from single stars. Both the BH and SN ejecta masses increase to about 80 M⊙ in our models when allowing for multiple mergers, for example, in initial triple-star systems, and they can be even higher at lower metallicities. Such high BH masses may fall into the pair-instability-SN mass gap and could help explain binary BH mergers involving very massive BHs as observed in GW190521. We further find that some of the BSG models explode as LBVs, which may lead to interacting SNe and possibly even superluminous SNe.

A MAC grid based FFT-AMIB solver for incompressible Stokes flows with interfaces and singular forces

In this paper, a second order accurate Augmented Matched Interface and Boundary (AMIB) method is introduced for solving the incompressible Stokes flows with interfaces and singular forces. Based on the MAC staggered grid for velocity and pressure, the zeroth order and first order jump conditions are repeatedly enforced in the AMIB scheme to generate fictitious values around the interface, which allow an accurate approximation of the Cartesian derivative jumps. By treating all jump quantities as auxiliary variables and coupling them with the corrected finite difference formulas, the Stokes equations can be discretized into an augmented system. The proposed FFT-AMIB solver does not need to take the pressure boundary condition into account. Moreover, in the Schur complement solution of the augmented system, the discrete Laplacian can be efficiently inverted by using the fast Fourier transform (FFT). Numerical results show that the FFT-AMIB solver is very efficient and can achieve second order accuracy for both velocity and pressure. The iteration number of Bi-CGSTAB in solving the resulting augmented system only weakly depends on the mesh size. When the interface is allowed to be moved under the surface tension, the proposed algorithm can maintain the divergence-free condition and area conservation very well.

QED corrections to the correlated relativistic energy: One-photon processes.

This work is a collection of initial calculations and formal considerations within the Salpeter-Sucher exact equal-time relativistic quantum electrodynamics framework. The calculations are carried out as preparation for the computation of pair, retardation, and radiative corrections to the relativistic energy of correlated two-spin-1/2-fermion systems. In this work, particular attention is paid to the retardation and the "one-loop" self-energy corrections, which are known to be among the largest corrections to the correlated relativistic energy. The theoretical development is supplemented with identifying formal connections to the non-relativistic quantum electrodynamics framework, which is based on a correlated but non-relativistic reference, as well as to the "1/Z approach," which is built on a relativistic but independent-particle zeroth order. The two complementary directions currently provide the theoretical framework for light atomic-molecular precision spectroscopy and heavy-atom phenomena. The present theoretical efforts pave the way for relativistic QED corrections to (explicitly) correlated relativistic computations.

On-axis complex-amplitude modulation for the generation of super-stable vector modes

We propose a technique to generate complex vector beams with high quality and stability. Our approach relies on the combination of complex amplitude modulation (CAM) and on-axis modulation, two techniques that seem incompatible at first glance. The first one produces scalar structured light fields in phase and amplitude with high accuracy, while the second one is preferred for generating vector beams of great stability although of reduced quality. Specifically, the idea behind our technique is to send the shaped light produced by CAM co-axially with the zeroth order, rather than diffracted to the first order, as it is commonly done. We first describe our technique, explaining the generation of the hologram and experimental setup to isolate the desired vector mode, and then present experimental results that corroborate our approach. We first address the quality of the generated beams using Stokes polarimetry to reconstruct their transverse polarisation distribution, and then compare their stability against the same mode produced using a Sagnac interferometric method. Our vector beams are of good quality and remarkably stable, two qualities that we expect will appeal to the community working with vector modes.

The effect of nonlocal disk processes on the volatile CHNOS budgets of planetesimal-forming material

Context. The bulk abundances of CHNOS-bearing species of a planet have a profound effect on its interior structure and evolution. Therefore, it is key to investigate the behavior of the local abundances of these elements in the solid phase in the earliest stages of planet formation, where micrometer-sized dust grows into larger and larger aggregates. However, the physical and chemical processes occurring in planet-forming disks that shape these abundances are highly coupled and nonlocal. Aims. We aim to quantify the effects of the interplay between dynamical processes (turbulent diffusion, dust settling and radial drift), collision processes (coagulation and fragmentation), and the adsorption and desorption of ices on the abundances of CHNOS in local disk solids as a function of position throughout the planet-forming region. Methods. We used SHAMPOO (Stochastic Monomer Processor), which tracks the ice budgets of CHNOS-bearing molecules of a dust monomer as it undergoes nonlocal disk processing in a Class I disk. We used a large set of individual monomer evolutionary trajectories to make inferences about the properties of the local dust populations via a stochastic analysis of 64 000 monomers on a preexisting spatial grid. Results. We find that spatially, monomers can travel larger distances farther out in the disk, leading to a larger spread in positions of origin for a dust population at, for example, r = 50 AU compared to r = 2 AU. However, chemically, the inner disk (r ≲ 10 AU) is more nonlocal due to the closer spacing of ice lines in this disk region. Although to zeroth order the bulk ice mantle composition of icy dust grains remains similar compared to a fully local dust population, the ice mass associated with individual chemical species can change significantly. The largest differences with local dust populations were found near ice lines where the collisional timescale is comparable to the adsorption and desorption timescales. Here, aggregates may become significantly depleted in ice as a consequence of microscopic collisional mixing, a previously unknown effect where monomers are stored away in aggregate interiors through rapid cycles of coagulation and fragmentation. Conclusions. Nonlocal ice processing in a diffusion-dominated, massive, smooth disk has the most significant impact on the inner disk (r ≲ 10 AU). Furthermore, microscopic collisional mixing can have a significant effect on the amounts of ice of individual species immediately behind their respective ice lines. This suggests that ice processing is highly coupled to collisional processing in this disk region, which implies that the interiors of dust aggregates must be considered and not just their surfaces.

Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data

In this paper we study an inverse boundary value problem for the biharmonic operator with first order perturbation. Our geometric setting is that of a bounded simply connected domain in the Euclidean space of dimension three or higher. Assuming that the inaccessible portion of the boundary is flat, and we have knowledge of the Dirichlet-to-Neumann map on the complement, we prove logarithmic type stability estimates for both the first and the zeroth order perturbation of the biharmonic operator.