Investigation of random thickness variations in chem-milled 2219-t37 aluminum final report
Random thickness variations in chemically milled aluminum alloy
METALLURGY↗
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Digital computers for compiling milling machine programs
Digital computer prototype for use in automatic control program for machining on a milling machine
DIGITAL COMPUTER↗
Study of factors affecting chemical milling Final report, 1 Jun. 1965 - 1 Jun. 1966
Nonuniform stock removal, quenching rate, cold working, hardness, and aging factors affect on chemical milling characteristics of aluminum alloys
QUENCHING↗
Yang-Mills observables: from $\mathrm{KMOC}$ to eikonal through $\mathrm{EFT}$
We obtain a conservative Hamiltonian describing the interactions of two charged bodies in Yang-Mills through $\mathcal{O}$ (α 2 ) and to all orders in velocity. Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory (EFT) to consider color-charged objects. These results are checked against the direct integration of the observables in the Kosower-Maybee-O’Connell (KMOC) formalism. At the order we consider we find that the linear and color impulses in a scattering event can be concisely described in terms of the eikonal phase, thus extending the domain of applicability of a formula originally proposed in the context of spinning particles.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Two-point sum-rules in three-dimensional Yang-Mills theory
We compute the stress-tensor two-point function in three-dimensional Yang-Mills theory to three-loops in perturbation theory. Using its calculable shape at high momenta, we test the notion that its Borel transform is saturated at low energies by the lowest glueball state(s). This assumption provides relatively stable estimates for the mass of the lightest glueball that we compare with lattice simulations. We also provide estimates for the coupling of the lightest glueball to the stress tensor. Along the way, we comment on the extent that such estimates are non-rigorous. Lastly, we discuss the possibility of applying the sum-rule analysis to two-point functions of higher-spin operators and obtain a crude approximation for the glueball couplings to these operators.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Integrands of less-supersymmetric Yang-Mills at one loop
We construct a prescriptive, bubble power-counting basis of one-loop integrands suitable for representing amplitude integrands in less-supersymmetric (1 ≤ $\mathcal{N}$ ≤ 4) Yang-Mills theory. With the exception of massless bubbles, all integrands have unambiguous, leading singularities as coefficients defined in field theory; for the massless bubbles on external legs, we find two natural choices which lead to different integrands that highlight distinct aspects of field theory. For concreteness, we give the all-multiplicity integrands for MHV amplitudes, and the split-helicity amplitude integrand for six-particle NMHV. The basis we construct is mostly pure and is divided into to separately UV- and IR-finite sectors of fixed transcendental weight, resulting in UV- and IR-finite ratio functions of n-particle helicity amplitudes.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Exact WKB and the quantum Seiberg-Witten curve for 4d $N$ = 2 pure SU(3) Yang-Mills. Abelianization
We investigate the exact WKB method for the quantum Seiberg-Witten curve of 4d N = 2 pure SU(3) Yang-Mills in the language of abelianization. The relevant differential equation is a third-order equation on $\mathbb{CP}^1$ with two irregular singularities. We employ the exact WKB method to study the solutions to such a third-order equation and the associated Stokes phenomena. We also investigate the exact quantization condition for a certain spectral problem. Moreover, exact WKB analysis leads us to consider new Darboux coordinates on a moduli space of flat SL(3,$\mathbb{C}$)-connections. In particular, in the weak coupling region we encounter coordinates of the higher length-twist type generalizing Fenchel-Nielsen coordinates. The Darboux coordinates are conjectured to admit asymptotic expansions given by the formal quantum periods series and we perform numerical analysis supporting this conjecture.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Recurrent features of amplitudes in planar $\mathcal{N}$ = 4 super Yang-Mills theory
The planar three-gluon form factor for the chiral stress tensor operator in planar maximally supersymmetric Yang-Mills theory is an analog of the Higgs-to-three-gluon scattering amplitude in QCD. The amplitude (symbol) bootstrap program has provided a wealth of high-loop perturbative data about this form factor, with results up to eight loops available. The symbol of the form factor at L loops is given by words of length 2L in six letters with associated integer coefficients. In this paper, we analyze this data, describing patterns of zero coefficients and relations between coefficients. We find many sequences of words whose coefficients are given by closed-form expressions which we expect to be valid at any loop order. Moreover, motivated by our previous machine-learning analysis, we identify simple recursion relations that relate the coefficient of a word to the coefficients of particular lower-loop words. These results open an exciting door for understanding scattering amplitudes at all loop orders.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Loop equation and exact soft anomalous dimension in $ \mathcal{N} $ = 4 super Yang-Mills
BPS Wilson loops in supersymmetric gauge theories have been the subjects of active research since they are often amenable to exact computation. So far most of the studies have focused on loops that do not intersect. In this paper, we derive exact results for intersecting 1/8 BPS Wilson loops in $ \mathcal{N} $ = 4 supersymmetric Yang-Mills theory, using a combination of supersymmetric localization and the loop equation in 2d gauge theory. The result is given by a novel matrix-model-like representation which couples multiple contour integrals and a Gaussian matrix model. We evaluate the integral at large N, and make contact with the string worldsheet description at strong coupling. As an application of our results, we compute exactly a small-angle limit (and more generally near-BPS limits) of the cross anomalous dimension which governs the UV divergence of intersecting Wilson lines. The same quantity describes the soft anomalous dimension of scattering amplitudes of W-bosons in the Coulomb branch.
't Hooftand Polyakov loops↗
On the symmetry TFT of Yang-Mills-Chern-Simons theory
Three-dimensional Yang-Mills-Chern-Simons theory has the peculiar property that its one-form symmetry defects have nontrivial braiding, namely they are charged under the same symmetry they generate, which is then anomalous. This poses a few puzzles in describing the corresponding Symmetry TFT in a four-dimensional bulk. First, the braiding between lines at the boundary seems to be ill-defined when such lines are pulled into the bulk. Second, the Symmetry TFT appears to be too trivial to allow for topological boundary conditions encoding all the different global variants. We show that both of these puzzles can be solved by including endable (tubular) surfaces in the class of bulk topological operators one has to consider. In this way, we are able to reproduce all global variants of the theory, with their symmetries and their anomalies. We check the validity of our proposal also against a top-down holographic realization of the same class of theories.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
\( \mathcal{N} \) = 4 supersymmetric Yang-Mills thermodynamics to order λ 2
We calculate the resummed perturbative free energy of \( \mathcal{N} \) = 4 supersymmetric Yang-Mills in four spacetime dimensions (SYM 4 , 4 ) through second order in the ’t Hooft coupling λ at finite temperature and zero chemical potential. Our final result is ultraviolet finite and all infrared divergences generated at three-loop level are canceled by summing over SYM 4 , 4 ring diagrams. Non-analytic terms at \( \mathcal{O} \) ( λ 3 / 2 ) and \( \mathcal{O} \) ( λ 2 log λ ) are generated by dressing the A 0 and scalar propagators. The gauge-field Debye mass m D and the scalar thermal mass M D are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of SYM 4 , 4 to \( \mathcal{O} \) ( λ 2 ). We compare our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Padé approximant that interpolates between the weak-coupling result and the large- N c strong-coupling result. Our results suggest that the \( \mathcal{O} \) ( λ 2 ) weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
One-loop central-emission vertex for two gluons in $\mathcal{N}$ = 4 super Yang-Mills theory
A necessary ingredient for extending the BFKL equation to next-to-next-to-leading logarithmic (NNLL) accuracy is the one-loop central emission vertex (CEV) for two gluons which are not strongly ordered in rapidity. Here we consider the one-loop six-gluon amplitude in $\mathcal{N}$ = 4 super Yang-Mills (SYM) theory in a central next-to-multi-Regge kinematic (NMRK) limit, we show that its dispersive part factorises in terms of the two-gluon CEV, and we use it to extract the one-loop two-gluon CEV for any helicity configuration within this theory. This is a component of the two-gluon CEV in QCD. Although computed in the NMRK limit, both the colour structure and the kinematic dependence of the two-gluon CEV capture much of the complexity of the six-gluon amplitudes in general kinematics. In fact, the transcendental functions of the latter can be conveniently written in terms of impact factors, trajectories, single-emission CEVs and a remainder, which is a function of the conformally invariant cross ratios which characterise the six-gluon amplitudes in planar $\mathcal{N}$ = 4 SYM. Finally, as expected, in the MRK limit the two-gluon CEV neatly factorises in terms of two single-emission CEVs.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Holography from lattice $\mathcal{N}$ = 4 super Yang-Mills
In this paper we use lattice simulation to study four dimensional $\mathcal{N}$ = 4 super Yang-Mills (SYM) theory. We have focused on the three color theory on lattices of size 12 4 and for ’t Hooft couplings up to λ = 40.0. Our lattice action is based on a discretization of the Marcus or GL twist of $\mathcal{N}$ = 4 SYM and retains one exact supersymmetry for non-zero lattice spacing. We show that lattice theory exists in a single non-Abelian Coulomb phase for all ’t Hooft couplings. Furthermore the static potential we obtain from correlators of Polyakov lines is in good agreement with that obtained from holography — specifically the potential has a Coulombic form with a coefficent that varies as the square root of the ’t Hooft coupling.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Two-loop HTL-resummed thermodynamics for $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory
We compute the two-loop hard-thermal-loop (HTL) resummed thermodynamic potential for \( \mathcal{N} \) = 4 supersymmetric Yang-Mills (SYM). Our final result is manifestly gauge-invariant and was renormalized using only simple vacuum energy, gluon mass, scalar mass, and quark mass counter terms. The HTL mass parameters m D , M D , and m q are then determined self-consistently using a variational prescription which results in a set of coupled gap equations. Based on this, we obtain the two-loop HTL-resummed thermodynamic functions of \( \mathcal{N} \) = 4 SYM. We compare our final result with known results obtained in the weak- and strong-coupling limits. We also compare to previously obtained approximately self-consistent HTL resummations and Padé approximants. We find that the two-loop HTL resummed results for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2 and is in agreement with previous approximately self-consistent HTL resummation results for λ ≲ 6.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Lattice $ \mathcal{N} $ = 4 super Yang-Mills at strong coupling
In this paper we present results from numerical simulations of N = 4 super Yang-Mills for two color gauge theory over a wide range of ’t Hooft coupling 0 < λ ≤ 30 using a supersymmetric lattice action. Numerical study of this lattice theory has been stymied until recently by both sign problems and the occurrence of lattice artifact phases at strong coupling. We have recently developed a new action that appears capable of solving both problems. The resulting action possesses just SU(2) rather than U(2) gauge symmetry. By explicit computations of the fermion Pfaffian we present evidence that the theory possesses no sign problem and exists in a single phase out to arbitrarily strong coupling. Furthermore, preliminary work shows that the logarithm of the supersymmetric Wilson loop varies as the square root of the ’t Hooft coupling λ for large λ in agreement with holographic predictions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Synergistic effects of chemical-free hydrothermal pretreatment on the recovery of cellulosic sugars and pectin from sugar mill-derived sugar beet pulp
Sugar mills processing sugar beet generate large amounts of sugar beet pulp (SBP), a carbohydrate-rich byproduct composed of 22–30% cellulose, 24–32 % hemicellulose, and 15-20% pectin. Mild, chemical-free hydrothermal pretreatment offers a promising approach to recover these compounds while minimizing pectin degradation, reducing chemical use, and lowering operating costs for value-added applications. This study evaluates the effects of chemical-free hydrothermal pretreatment on cellulosic sugars recovery and its synergy with subsequent pectin extraction under pretreatment conditions ranging from 80°C to 120°C for 15-45 min. Results show that increasing pretreatment severity preserved most glucans with 4% decrease in galacturonan content. Optimal pretreatment (100°C for 45 min) followed by enzymatic hydrolysis achieved the best glucose (95%) and pentose (74%) yields, while galacturonan remained concentrated in the residual solids. Subsequent citric acid extraction at 80°C for 3 hr and a solid-to-liquid ratio of 1:15 yielded up to 85% pectin, significantly lowering water, chemical, and energy requirements compared to conventional industrial extraction. The integration of mild hydrothermal pretreatment with enzymatic hydrolysis thus maximized sugar recovery and enabled efficient downstream pectin extraction without compromising product yields. These findings advance low-impact valorization strategies to reinforce SBP’s values in biorefinery.
09 - BIOMASS FUELS↗
Stability boundary and optimal operating parameter identification in milling using Bayesian learning
Here, this paper describes a novel Bayesian learning approach for stability boundary and optimal parameter identification in milling without the knowledge of the underlying tool dynamics or material cutting force coefficients. The paper is divided into two parts. First, a Bayesian learning method for stability lobe identification using test results is described. Each axial depth and spindle speed combination is characterized by a probability of stability which is updated using Bayes’ rule when a test result (stable or unstable) is made available. A novel likelihood function is defined which incorporates knowledge of the stability behavior. Numerical results show convergence to the analytical stability lobe diagram. Second, an adaptive experimental strategy to identify optimal operating parameters that maximize material removal rate is described. Numerical evaluation shows convergence to the optimal operating point with error less than 15 % within ten tests on average. The approach is validated using experimental results. Results show that the proposed method is an efficient and robust learning method to identify the stability lobe diagram and optimal operating parameters with a limited number of tests/data points.
Bayesian machine learning↗
Effects of magnetic field annealing on the hard magnetic properties of milled Nd-Fe-B powders
In this study, we report the effect of magnetic field annealing (MA) in relieving the stress induced during the milling of Nd-Fe-B sintered magnets. The effect of MA processing parameters and particle size on the magnetic properties were investigated. Based on the results, magnetic field annealing is more effective in improving the magnetic properties of larger size particles, compared to finer particles. Our computational study on the role of particle surface defects in bi-modal particle distribution agrees with results obtained experimentally. In conclusion, magnetic field annealed powder has been successfully used to develop 4.6 g.cm -3 density bonded magnets with 75 vol% of magnetic powder and polyamide 12 (nylon 12) polymer binder resulting in 11.3 MGOe energy product.
36 MATERIALS SCIENCE↗