The factorization theorems of quantum chromodynamics (QCD) apply equally well to most simple quantum field theories that require renormalization but where direct calculations are much more straightforward. Working with these simpler theories is convenient for stress-testing the limits of the factorization program and for examining general properties of the parton density functions (pdfs) or other correlation functions that might be necessary for a factorized description of a process. With this view in mind, we review the steps of factorization in a real scalar Yukawa field theory for both deep inelastic scattering (DIS) and semi-inclusive deep inelastic scattering (SIDIS) cross sections. In the case of SIDIS, we illustrate how to separate the small transverse momentum region, where transverse momentum dependent (TMD) pdfs are needed, from a purely collinear large transverse momentum region, and we examine the influence of subleading power corrections. We also review the steps for formulating TMD factorization in transverse coordinate space, and we study the effect of transforming to the well-known $b_*$-scheme. Within the Yukawa theory, we investigate the consequences of switching to a generalized parton model (GPM) approach, and compare with a fully factorized approach. Our results highlight the need to address similar or analogous issues in QCD.

Future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in the region where the partonic structure of the nucleon is dominated by the valence quarks. One of the main goals is to constrain the quark transversity distributions. We apply recent theoretical advances of the global QCD extraction of the transversity distributions to study the impact of future experimental data from the SoLID experiments. Especially, we develop a simple strategy based on the Hessian matrix analysis that allows one to estimate the uncertainties of the transversity quark distributions and their tensor charges extracted from SoLID data simulation. We find that the SoLID measurements with the proton and the effective neutron targets can improve the precision of the u- and d-quark transversity distributions up to one order of magnitude in the range 0.05 < x < 0.6.

We present a phenomenological study on the role of charm contribution and $SU(2)$ isospin symmetry in the extraction of the $\Lambda$ polarizing fragmentation functions from $e^+e^- \to \Lambda^\uparrow (\bar\Lambda^\uparrow) \,h + X$ annihilation processes. We adopt the well-established transverse-momentum-dependent factorization formalism, within the Collins-Soper-Sterman evolution scheme at next-to-leading logarithm accuracy, carefully exploiting the role of the nonperturbative component of the polarizing fragmentation function. We then discuss the impact of these results on the predictions for transverse $\Lambda$, $\bar{\Lambda}$ polarization in semi-inclusive deep inelastic scattering processes at typical energies of the future Electron-Ion Collider.

This paper considers solving the unequal area Dynamic Facility Layout Problem (DFLP) using a zone-based structure. Zone-based layouts have significant advantages, such as being easily transferable to a detailed layout with innately included possible aisle structures; therefore, they can be fitted to the unique needs of the layout designers. The unequal area DFLP is modeled and solved using a zone-based structure, which is referred to as ZDFLP, where the dimensions of the departments and material handling system input/output (I/O) points are decision variables. A two-phase matheuristic, which directly operates on Problem ZDFLP without requiring an encoding scheme of the problem, is proposed to solve the ZDFLP with promising results.

It is argued that the definition of the twist-3 transverse momentum dependent correlation functions must be modified if they contain light-like Wilson lines. In the framework of a simple spectator model of the nucleon we show explicitly the presence of a light-cone divergence for a specific twist-3 time-reversal odd parton density. This divergence emerges for all eight twist-3 T-odd correlators and appears also in the case of a quark target in perturbative QCD. The divergence can be removed by using non-light-like Wilson lines. Based on our results we argue that currently there exists no established factorization formula for transverse momentum dependent twist-3 observables in semi-inclusive DIS and related processes.

Research on environmental risk modeling relies on numerous indicators to quantify the magnitude and frequency of extreme climate events, their ecological, economic, and social impacts, and the coping mechanisms that can reduce or mitigate their adverse effects. Index-based approaches significantly simplify the process of quantifying, comparing, and monitoring risks associated with other natural hazards, as a large set of indicators can be condensed into a few key performance indicators. Data fusion techniques are often used in conjunction with expert opinions to develop key performance indicators. This paper discusses alternative methods to combine data from multiple indicators, with an emphasis on their use-case scenarios, underlying assumptions, data requirements, advantages, and limitations. The paper demonstrates the application of these data fusion methods through examples from current risk and resilience models and simplified datasets. Simulations are conducted to identify their strengths and weaknesses under various scenarios. Finally, a real-life example illustrates how these data fusion techniques can be applied to inform policy recommendations in the context of drought resilience and sustainability.

We summarize the most significant aspects in the study of transverse spin phenomena over the last few decades, focusing on Semi-Inclusive Deep Inelastic Scattering processes and hadronic production in $e^+e^-$ annihilations. The phenomenology of transverse momentum dependent distribution and fragmentation functions will be reviewed in an in-depth analysis of the most recent developments and of the future perspectives.

This paper proposes a single-domain dual-reciprocity inclusion-based boundary element method (DR-iBEM) for a three-dimensional fully bonded bi-layered composite embedded with ellipsoidal inhomogeneities under transient/harmonic thermal loads. The heat equation is interpreted as a static one containing time- and frequency-dependent nonhomogeneous source terms, which is similar to eigen-fields but is transformed into a boundary integral by the dual-reciprocity method. Using the steady-state bimaterial Green's function, boundary integral equations are proposed to take into account continuity conditions of temperature and heat flux, which avoids setting up any continuity equations at the bimaterial interface. Eigen-temperature-gradients and eigen-heat-source are introduced to simulate the material mismatch in thermal conductivity and heat capacity, respectively. The DR-iBEM algorithm is particularly suitable for investigating the transient and harmonic thermal behaviors of bi-layered composites and is verified by the finite element method (FEM). Numerical comparison with the FEM demonstrates its robustness and accuracy. The method has been applied to a functionally graded material as a bimaterial with graded particle distributions, where particle size and gradation effects are evaluated.

In this Letter, we investigate the spontaneous transverse polarization of $\Lambda$ hyperons produced in unpolarized $pp$ collisions inside a jet, by adopting a TMD approach where transverse momentum effects are included only in the fragmentation process. We will present predictions based on the parametrizations of the $\Lambda$ polarizing fragmentation function as extracted from fits to Belle $e^+e^-$ data. These estimates will be compared against preliminary STAR data. We will then be able to explore the universality properties of the quark polarizing fragmentation function and, for the first time, the role of its gluon counterpart.

In this paper we study transverse polarization of $\Lambda$ hyperons in single-inclusive leptonic annihilation. We show that when the transverse momentum of the $\Lambda$ baryon is measured with respect to the thrust axis, a transverse momentum dependent (TMD) factorization formalism is required and the polarization is generated by the TMD polarizing fragmentation function (TMD PFF), $D_{1T}^\perp$. However, when the transverse momentum of the $\Lambda$ baryon is measured with respect to the momentum of the initial leptons, a collinear twist-3 formalism is required and the polarization is generated by the intrinsic collinear twist-3 fragmentation function $D_{T}$. Thus while these measurements differ from one another only by a change in the measurement axis, they probe different distribution functions. Recently, Belle measured a significant polarization in single-inclusive $\Lambda$ baryon production as a function of the transverse momentum with respect to the thrust axis. However, this data can in principle be re-analyzed to measure the polarization as a function of the transverse momentum of the $\Lambda$ baryon with respect to the lepton pair. This observable could be the first significant probe of the function, $D_{T}$. In this paper, we first develop a TMD formalism for $\Lambda$ polarization; we then present a recent twist-3 formalism that was established to describe $\Lambda$ polarization. Using the TMD formalism, we demonstrate that the $\Lambda$ polarization at OPAL and Belle can be described using the twist-2 TMD factorization formalism. Finally, we make a theoretical prediction for this polarization in the collinear twist-3 formalism at Belle.