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↗
On the binding energy of He(n)+, for n = 2-7
The atomization energy of small positively charged He clusters has been studied using ab initio methods that include correlation. The atomization energy increases monotonically with cluster size. The inclusion of correlation changes the nature of the bonding and hence changes the structure of the most stable cluster.
Rosi, Marzio↗
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↗
On the problem of modeling for parameter identification in distributed structures
Structures are often characterized by parameters, such as mass and stiffness, that are spatially distributed. Parameter identification of distributed structures is subject to many of the difficulties involved in the modeling problem, and the choice of the model can greatly affect the results of the parameter identification process. Analogously to control spillover in the control of distributed-parameter systems, identification spillover is shown to exist as well and its effect is to degrade the parameter estimates. Moreover, as in modeling by the Rayleigh-Ritz method, it is shown that, for a Rayleigh-Ritz type identification algorithm, an inclusion principle exists in the identification of distributed-parameter systems as well, so that the identified natural frequencies approach the actual natural frequencies monotonically from above.
Norris, Mark A.↗
A perturbation technique for parameter identification in distributed structures
Structures are often characterized by parameters, such as mass and stiffness, that are spatially distributed. Parameter identification of distributed structures is subject to many of the difficulties involved in the modeling problem, and the choice of the model can greatly affect the results of the parameter identification process. Analogously to control spillover in the control of distributed-parameter systems, identification spillover is shown to exist as well and its effect is to degrade the parameter estimates. Moreover, as in modeling by the Rayleigh-Ritz method, it is shown that, for a Rayleigh-Ritz type identification algorithm, an inclusion principle exists in the identification of distributed-parameter systems as well, so that the identified natural frequencies approach the actual natural frequencies monotonically from above.
Meirovitch, L.↗
On the problem of modeling for parameter identification in distributed structures
Structures are often characterized by parameters, such as mass and stiffness, that are spatially distributed. Parameter identification of distributed structures is subject to many of the difficulties involved in the modeling problem, and the choice of the model can greatly affect the results of the parameter identification process. Analogously to control spillover in the control of distributed-parameter systems, identification spillover is shown to exist as well and its effect is to degrade the parameter estimates. Moreover, as in modeling by the Rayleigh-Ritz method, it is shown that, for a Rayleigh-Ritz type identification algorithm, an inclusion principle exists in the identification of distributed-parameter systems as well, so that the identified natural frequencies approach the actual natural frequencies monotonically from above.
Norris, Mark A.↗
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↗
Thermally induced damage in composite space structure: Predictive methodology and experimental correlation
A general analysis method is presented to predict matrix cracks in all plies of a composite laminate, and resulting degraded laminate properties, as functions of temperature or thermal cycles. A shear lag solution of the stresses in the vicinity of cracks and a fracture mechanics crack formation criteria are used to predict cracks. Damage is modeled incrementally, which allows the inclusion of the effects of temperature dependent material properties and softening of the laminate due to previous cracking. The analysis is incorporated into an easy-to-use computer program. The analysis is correlated with experimentally measured crack densities in a variety of laminates exposed to monotonically decreasing temperatures. Crack densities are measured at the edges of specimens by microscopic inspection, and throughout the specimen volumes by x-ray and sanding down of the edges. Correlation between the analytical results and the crack densities in the interiors of the specimens was quite good. Crack densities measured at specimen edges did not agree with internal crack densities (or analyses) in some cases. A free-edge stress analysis clarified the reasons for these discrepancies.
Park, Cecelia↗
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↗