Variance-Reduced Splitting Schemes for Monotone Stochastic Generalized Equations
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Automation & Control Systems↗
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Stochastic projective splitting
Here, we present a new, stochastic variant of the projective splitting (PS) family of algorithms for inclusion problems involving the sum of any finite number of maximal monotone operators. This new variant uses a stochastic oracle to evaluate one of the operators, which is assumed to be Lipschitz continuous, and (deterministic) resolvents to process the remaining operators. Our proposal is the first version of PS with such stochastic capabilities. We envision the primary application being machine learning (ML) problems, with the method’s stochastic features facilitating “mini-batch” sampling of datasets. Since it uses a monotone operator formulation, the method can handle not only Lipschitz-smooth loss minimization, but also min–max and noncooperative game formulations, with better convergence properties than the gradient descent-ascent methods commonly applied in such settings. The proposed method can handle any number of constraints and nonsmooth regularizers via projection and proximal operators. We prove almost-sure convergence of the iterates to a solution and a convergence rate result for the expected residual, and close with numerical experiments on a distributionally robust sparse logistic regression problem.
97 MATHEMATICS AND COMPUTING↗
Large N algebras and generalized entropy
We construct a Type II ∞ von Neumann algebra that describes the large N physics of single-trace operators in AdS/CFT in the microcanonical ensemble, where there is no need to include perturbative 1/N corrections. Using only the extrapolate dictionary, we show that the entropy of semiclassical states on this algebra is holographically dual to the generalized entropy of the black hole bifurcation surface. From a boundary perspective, this constitutes a derivation of a special case of the QES prescription without any use of Euclidean gravity or replicas; from a purely bulk perspective, it is a derivation of the quantum-corrected Bekenstein-Hawking formula as the entropy of an explicit algebra in the G → 0 limit of Lorentzian effective field theory quantum gravity. In a limit where a black hole is first allowed to equilibrate and then is later potentially re-excited, we show that the generalized second law is a direct consequence of the monotonicity of the entropy of algebras under trace-preserving inclusions. Finally, by considering excitations that are separated by more than a scrambling time we construct a “free product” von Neumann algebra that describes the semiclassical physics of long wormholes supported by shocks. We compute Rényi entropies for this algebra and show that they are equal to a sum over saddles associated to quantum extremal surfaces in the wormhole. Surprisingly, however, the saddles associated to “bulge” quantum extremal surfaces contribute with a negative sign.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Enhanced signal of momentum broadening in hard splittings for $γ$-tagged jets in a multistage approach
We investigate medium-induced modifications to jet substructure observables that characterize hard splitting patterns in central Pb-Pb collisions at the top energy of the Large Hadron Collider (LHC). Using a multistage Monte Carlo simulation of in-medium jet shower evolution, we explore flavor-dependent medium effects through simulations of inclusive and $γ$-tagged jets. The results show that quark jets undergo a non-monotonic modification compared to gluon jets in observables such as the Pb-Pb to $p$-$p$ ratio of the Soft Drop prong angle $r_g$, the relative prong transverse momentum $k_{T,g}$ and the groomed mass $m_g$ distributions. Due to this non-monotonic modification, $γ$-tagged jets, enriched in quark jets, provide surprisingly clear signals of medium-induced structural modifications, distinct from effects dominated by selection bias. This work highlights the potential of hard substructures in $γ$-tagged jets as powerful tools for probing the jet-medium interactions in high-energy heavy-ion collisions. All simulations for $γ$-tagged jet analyses carried out in this paper used triggered events containing at least one hard photon, which highlights the utility of these observables for future Bayesian analysis.
FOS: Physical sciences↗
Super-time-stepping schemes for parabolic equations with boundary conditions
In this work, we present a super-time-stepping scheme for numerically solving parabolic partial differential equations with Dirichlet boundary conditions (BC). Using the general Forward Euler scheme, one can show that by taking varying step sizes there is the potential of propagating the solution forward in time by a greater amount than with uniform step sizes, while maintaining the same order of accuracy. As shown in previous works, if one further requires that the scheme have the Convex Monotone Property (CMP), then there exists a scheme which results in linear, monotone stability of the solution. This monotone stability is highly desirable in many physical situations, such as thermal diffusion, where the physical system will not oscillate, but will behave monotonically. However, the schemes devised in previous works do not include situations that have a boundary condition, and the inclusion of boundary conditions will henceforth be our focus. It is shown that a particular Runge-Kutta-Gegenbauer class of schemes [5] will maintain the CMP even in the presence of Dirichlet BC.
97 MATHEMATICS AND COMPUTING↗
In situ, 3D characterization of the deformation mechanics of a superelastic NiTi shape memory alloy single crystal under multiscale constraint
Microstructural elements in NiTi shape memory alloys (SMAs) – precipitates, phase boundaries, inclusions, grain boundaries – can be viewed as sources of multiscale constraint that influence their deformation response. In this paper, we characterized in situ, and in 3D, the deformation and the evolution of microstructure during a tension test in a superelastic NiTi specimen containing some of these sources of constraint. The method used was far-field high-energy X-ray diffraction microscopy (ff-HEDM), complemented by electron microscopy. We simulated the local stress state in the specimen using a microstructural model informed by the experimental data. Using these combined microstructure, deformation, and stress data, we report three phenomena, and relate them to specific sources of constraint. During initial elastic loading, axial lattice strain in austenite increased monotonically. On partial stress-induced phase transformation to martensite, the stress redistributed to both phases leading to a stress relaxation in austenite. The specimen contained a dense distribution of inclusions, which led to the activation of martensite habit plane variants that produce less than theoretical maximum transformation strain. Large Ni 4 Ti 3 precipitates potentially contributed to the poor transformation response. Under load, proportional gradients in local rotation and elastic stretch developed in the martensite phase, because of the constraint at phase interfaces. Finally, this combined ff-HEDM, electron microscopy, microstructural simulation toolbox provides a versatile method to understand the effect of constraint on inelastic deformation in other alloys with hierarchical microstructure.
36 MATERIALS SCIENCE↗
Distinct Impacts of Aerosols on an Evolving Continental Cloud Complex during the RACORO Field Campaign
In this study, a continental cloud complex, consisting of shallow cumuli, a deep convective cloud (DCC), and stratus, is simulated by a cloud-resolving Weather Research and Forecasting Model to investigate the aerosol microphysical effect (AME) and aerosol radiative effect (ARE) on the various cloud regimes and their transitions during the Department of Energy Routine Atmospheric Radiation Measurement Aerial Facility Clouds with Low Optical Water Depths Optical Radiative Observations (RACORO) campaign. Under an elevated aerosol loading with AME only, a reduced cloudiness for the shallow cumuli and stratus resulted from more droplet evaporation competing with suppressed precipitation, but an enhanced cloudiness for the DCC is attributed to more condensation. With the inclusion of ARE, the shallow cumuli are suppressed owing to the thermodynamic effects of light-absorbing aerosols. The responses of DCC and stratus to aerosols are monotonic with AME only but nonmonotonic with both AME and ARE. The DCC is invigorated because of favorable convection and moisture conditions at night induced by daytime ARE, via the so-called aerosol-enhanced conditional instability mechanism. Finally, the results reveal that the overall aerosol effects on the cloud complex are distinct from the individual cloud types, highlighting that the aerosol–cloud interactions for diverse cloud regimes and their transitions need to be evaluated to assess the regional and global climatic impacts.
54 ENVIRONMENTAL SCIENCES↗
Many-Body Effects in FeN4 Center Embedded in Graphene
We introduce a computational approach to study porphyrin-like transition metal complexes, bridging density functional theory and exact many-body techniques, such as the density matrix renormalization group (DMRG). We first derive a multi-orbital Anderson impurity Hamiltonian starting from first principles considerations that qualitatively reproduce generalized gradient approximation (GGA)+U results when ignoring inter-orbital Coulomb repulsion U ′ and Hund exchange J. An exact canonical transformation is used to reduce the dimensionality of the problem and make it amenable to DMRG calculations, including all many-body terms (both intra- and inter-orbital), which are treated in a numerically exact way. We apply this technique to FeN 4 centers in graphene and show that the inclusion of these terms has dramatic effects: as the iron orbitals become single occupied due to the Coulomb repulsion, the inter-orbital interaction further reduces the occupation, yielding a non-monotonic behavior of the magnetic moment as a function of the interactions, with maximum polarization only in a small window at intermediate values of the parameters. Furthermore, U ′ changes the relative position of the peaks in the density of states, particularly on the iron d z 2 orbital, which is expected to affect the binding of ligands greatly.
36 MATERIALS SCIENCE↗
3D-Bioprinted Marine Bacteria for the Degradation of Polyhydroxybutyrate Bioplastics
The severe, long-lasting harm caused by plastic pollution to marine ecosystems and coastal economies has led to the development of biodegradable plastics; however, their limited decomposition in marine environments remains a challenge. Here, technologies are presented for creating 3D-bioprinted living materials as a proof of concept for bioplastic degradation, with specific use in marine environments. The approach developed here integrates the halotolerant bioplastic-degrading bacterium Bacillus sp. NRRL B- 14911 into alginate-based bio-ink to print an engineered living material (ELM) termed a “bio-sticker.” Quantification of bacteria viability reveals that bioprinted marine bacteria survive within biostickers for more than 3 weeks. The rate at which the biostickers degrade the bioplastic polyhydroxybutyrate (PHB) can be tuned by altering biosticker biomass concentration, bioplastic concentration, or incubation temperature. Biostickers that are transferred to a different PHB sample still retain high biodegradation activity, demonstrating their reusability. Strain sweep oscillatory tests demonstrate that the biostickers display predominantly viscoelastic behavior. Monotonic tensile tests indicate that the elastic modulus and the adhesion of the biostickers are not negatively impacted by bacteria growth or incubation temperature. This work paves the way for the development of ELMs to facilitate the inclusion of bioplastics within the blue economy, promoting the emergence of more sustainable and ecofriendly materials.
3D bioprinting↗
Magnetostrictive loss reduction through stress relief annealing in an FeNi-based metal amorphous nanocomposite
FeNi-based metal amorphous nanocomposite alloys are emerging soft magnetic materials with promise for high-speed motor applications. Here we demonstrate a technique to optimize magnetic properties in toroidal cores wound from strain annealed (Fe 70 Ni 30 ) 80 Nb 4 Si 2 B 14 amorphous metal ribbon (AMR). In-line strain annealing (SA) of the AMR yields a strip permeability that monotonically decreases with increasing SA tensions. After winding into toroidal cores, dramatic changes in magnetic properties are observed and determined to be of magnetostrictive origin. A procedure to re-anneal wound toroidal cores to reduce hysteresis and reverse magnetostrictive effects is developed inclusive of casting curvature effects. Here, we investigate re-annealing temperatures between 300 – 470 °C for cores produced from each SA condition. Magnetic core loss, W L , coercivity, H c , squareness ratio, K r , and permeability, µ r , are measured as a function of (stress relief) re-annealing temperature to optimally achieve W 1T,400Hz = 0.51 W/kg, H c = 2.42 A/m, K r = 0.22, and µ r = 35,300.
36 MATERIALS SCIENCE↗
Recovering the QNEC from the ANEC
We study the relative entropy in QFT comparing the vacuum state to a special family of purifications determined by an input state and constructed using relative modular flow. We use this to prove a conjecture by Wall that relates the shape derivative of relative entropy to a variational expression over the averaged null energy (ANE) of possible purifications. Furthermore, this variational expression can be used to easily prove the quantum null energy condition (QNEC). We formulate Wall’s conjecture as a theorem pertaining to operator algebras satisfying the properties of a half-sided modular inclusion, with the additional assumption that the input state has finite averaged null energy. We also give a new derivation of the strong superadditivity property of relative entropy in this con- text. We speculate about possible connections to the recent methods used to strengthen monotonicity of relative entropy with recovery maps.
97 MATHEMATICS AND COMPUTING↗
Model dependence of the γZ dispersion correction to the parity-violating asymmetry in elastic ep scattering
Not Available
Gorchtein, Mikhail↗
Formation of microcraters and hierarchically-organized surface structures in TiNi shape memory alloy irradiated with a low-energy, high-current electron beam
The regularities of surface cratering in TiNi alloy irradiated with a low-energy, high-current electron beam (LEHCEB) in dependence on energy density and number of pulses are studied. LEHCEB processing of TiNi samples was carried out using RITM-SP facility. Energy density E{sub s} was varied from 1 to 5 J/cm{sup 2}, pulse duration was 2.5–3.0 μs, the number of pulses n = 1–128. The dominant role of non-metallic inclusions [mainly, TiC(O)] in the nucleation of microcraters was found. It was revealed that at small number of pulses (n = 2), an increase in energy density leads both to increasing average diameter and density of microcraters. An increase in the number of pulses leads to a monotonic decrease in density of microcraters, and, therefore, that of the proportion of the area occupied by microcraters, as well as a decrease in the surface roughness. The multiple LEHCEB melting of TiNi alloy in crater-free modes enables to form quasi-periodical, hierarchically-organized microsized surface structures.
36 MATERIALS SCIENCE↗
Correlation between inter-spin interaction and molecular dynamics of organic radicals in organic 1D nanochannels
One-dimensional (1D) molecular chains of 4-substituted-2,2,6,6-tetramethyl-1-piperidinyloxyl (4-X-TEMPO) radicals were constructed in the crystalline 1D nanochannels of 2,4,6-tris(4-chlorophenoxy)-1,3,5-triazine (CLPOT) used as a template. The ESR spectra of CLPOT inclusion compounds (ICs) using 4-X-TEMPO were examined on the basis of spectral simulation using EasySpin program package for simulating and fitting ESR spectra. The ESR spectra of [(CLPOT){sub 2}-(TEMPO){sub 1.0}] IC were isotropic in the total range of temperatures. The peak-to-peak line width (ΔB{sub pp}) became monotonically narrower from 2.8 to 1.3 mT with increase in temperature in the range of 4.2–298 K. The effect of the rotational diffusion motion of TEMPO radicals in the CLPOT nanochannels for the inter-spin interaction of the [(CLPOT){sub 2}-(TEMPO){sub 1.0}] IC was found to be smaller than the case of [(TPP){sub 2}−(TEMPO){sub 1.0}] IC (TPP = tris(o-phenylenedioxy)cyclotriphosphazene) reported in our previous study. The ΔB{sub pp} of the [(CLPOT){sub 2}-(TEMPO){sub 1.0}] IC in the whole range of temperatures was much narrower than the estimation to be based on the Van Vleck’s formula for the second moment of the rigid lattice model where the electron spin can be considered as fixed; 11 mT of Gaussian line-width component. This suggests the possibility of exchange narrowing in the 1D organic-radical chains of the [(CLPOT){sub 2}-(TEMPO){sub 1.0}] IC. On the other hand, the ESR spectra of [(CLPOT){sub 2}-(MeO-TEMPO){sub 0.41}] IC (MeO-TEMPO = 4-methoxy-TEMPO) were reproduced by a superposition of major broad isotropic adsorption line and minor temperature-dependent modulated triplet component. This suggests that the IC has the part of 1D organic-radical chains and MeO-TEMPO molecules isolated in the CLPOT nanochannels.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Formulation and characterization of a continuous crystal lattice orientation finite element method (LOFEM) and its application to dislocation fields
We report that since the 1950s, a large body of work has been published on connecting the curvature of a crystal lattice to geometrically necessary dislocations densities of a crystal lattice. Studying dislocation transmission through grains and across their boundaries requires the lattice curvature to be preserved. However, traditional crystal plasticity models and their numerical implementations do not formally preserve lattice curvature. In this paper, a continuous crystal lattice orientation finite element method (LOFEM) is proposed to rectify this impediment to the inclusion of dislocation-based constitutive models. The methodology is first presented, and then it is demonstrated for tension and compression deformations of a copper polycrystal. It is shown that under the same deformation histories, the lattice continuity constraint alters the evolving state in comparison to the traditional approach, including retarding the rate at which the crystallographic texture strengthens under monotonic deformation. Lastly, taking advantage of the finite element representation of the lattice orientation, the Nye tensor is computed on lattices misoriented by deformation and is subsequently used to compute evolving dislocation density distributions.
36 MATERIALS SCIENCE↗
MULTI-DIMENSIONAL SIMULATIONS OF ROTATING PAIR-INSTABILITY SUPERNOVAE
We study the effects of rotation on the dynamics, energetics, and {sup 56}Ni production of pair instability supernova (PISN) explosions by performing rotating two-dimensional ({sup 2}.5D{sup )} hydrodynamics simulations. We calculate the evolution of eight low-metallicity (Z = 10{sup –3}, 10{sup –4} Z{sub ☉}) massive (135-245 M{sub ☉}) PISN progenitors with initial surface rotational velocities of 50% of the critical Keplerian value using the stellar evolution code MESA. We allow for both the inclusion and the omission of the effects of magnetic fields in the angular momentum transport and in chemical mixing, resulting in slowly rotating and rapidly rotating final carbon-oxygen cores, respectively. Increased rotation for carbon-oxygen cores of the same mass and chemical stratification leads to less energetic PISN explosions that produce smaller amounts of {sup 56}Ni due to the effect of the angular momentum barrier that develops and slows the dynamical collapse. We find a non-monotonic dependence of {sup 56}Ni production on rotational velocity in situations when smoother composition gradients form at the outer edge of the rotating cores. In these cases, the PISN energetics are determined by the competition of two factors: the extent of chemical mixing in the outer layers of the core due to the effects of rotation in the progenitor evolution and the development of angular momentum support against collapse. Our 2.5D PISN simulations with rotation are the first presented in the literature. They reveal hydrodynamic instabilities in several regions of the exploding star and increased explosion asymmetries with higher core rotational velocity.
79 ASTRONOMY AND ASTROPHYSICS↗
The Influence of Temperature on the Cyclic Properties of the Transversely Isotropic Nanocomposite System Under Kinematic Harmonic Loading
A micromechanical model is developed to determine the effective inelastic properties of nanocomposites under monoharmonic deformation by taking into account the detailed microstructural geometries and constitutive models of the constituents. By using the correspondence principle in viscoelasticity and the modified Mori–Tanaka method, the effects of interface between the inclusion and the matrix are taken into account. By applying the developed model, we perform the numerical analysis aimed at the determination of complex moduli for a polymeric nanocomposite reinforced with nanofibers composed from carbon nanotubes under the isothermal conditions. The dependences of complex moduli on temperature and the amplitude of strain intensity are analyzed. The composites reinforced with unidirectionally aligned nanofibers are considered. The accumulated results demonstrate a strong dependence of the storage and loss moduli on temperature within a broad temperature range. The storage and loss moduli are found to monotonically increase with the volume fraction of nanofibers. At the same time, they decrease as temperature increases. The obtained results show that the strength of material decreases as temperature increases in the elastic and inelastic regions and the inelastic behavior occurs for lower strain amplitude as temperature increases.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Systematic study of azimuthal anisotropy in Cu + Cu and Au + Au collisions at √s NN = 62.4 and 200 GeV
We have studied the dependence of azimuthal anisotropy v 2 for inclusive and identified charged hadrons in Au+Au and Cu+Cu collisions on collision energy, species, and centrality. The values of v 2 as a function of transverse momentum pT and centrality in Au+Au collisions at √s NN =200 and 62.4 GeV are the same within uncertainties. However, in Cu+Cu collisions we observe a decrease in v 2 values as the collision energy is reduced from 200 to 62.4 GeV. The decrease is larger in the more peripheral collisions. By examining both Au+Au and Cu+Cu collisions we find that v 2 depends both on eccentricity and the number of participants, N part . We observe that v 2 divided by eccentricity (ε) monotonically increases with N part and scales as N 1/3 part . Thus, the Cu+Cu data at 62.4 GeV falls below the other scaled v 2 data. For identified hadrons, v 2 divided by the number of constituent quarks nq is independent of hadron species as a function of transverse kinetic energy KE T =m T –m between 0.1 T /n q <1 GeV. Combining all of the above scaling and normalizations, we observe a near-universal scaling, with the exception of the Cu+Cu data at 62.4 GeV, of v 2 /(n q ∙ε∙N 1/3 part ) vs KE T /n q for all measured particles.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗