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The well-studied red-blue pebble game models the execution of an arbitrary computational DAG by a single processor over a two-level memory hierarchy. We present a natural generalization to a multiprocessor setting where each processor has its own limited fast memory, and all processors share unlimited slow memory. To our knowledge, this is the first thorough study that combines pebbling and DAG scheduling problems, capturing the computation of general workloads on multiple processors with memory constraints and communication costs. Our pebbling model enables us to analyze trade-offs between workload balancing, communication and memory limitations, and it captures real-world factors such as superlinear speedups due to parallelization. Our results include upper and lower bounds on the pebbling cost, an analysis of a greedy pebbling strategy, and an extension of NP-hardness results for specific DAG classes from simpler models. For our main technical contribution, we show two inapproximability results that already hold for the long-standing problem of standard red-blue pebbling: (i) the optimal I/O cost cannot be approximated to any finite factor, and (ii) the optimal total cost (I/O+computation) can only be approximated to a limited constant factor, i.e., it does not allow for a polynomial-time approximation scheme. These results also carry over naturally to our multiprocessor pebbling model.

We consider divergence form operators with complex coefficients on an open subset of Euclidean space. Boundary conditions in the corresponding parabolic problem are dynamical, that is, the time derivative appears on the boundary. As a matter of fact, the elliptic operator and its semigroup act simultaneously in the interior and on the boundary. We show that the elliptic operator has a bounded $\mathrm{H}^\infty$-calculus in $\mathrm{L}^p$ if the coefficients satisfy a $p$-adapted ellipticity condition. A major challenge in the proof is that different parts of the spatial domain of the operator have different dimensions. Our strategy relies on extending a contractivity criterion due to Nittka and a non-linear heat flow method recently popularized by Carbonaro-Dragi\v{c}evi\'c to our setting., Comment: 29 pages, 1 figure

Fiber-reinforced polymer composite (FRPC) materials are used extensively in various industries, such as aerospace, automobiles, and electronics packaging, due to their remarkable specific strength and desirable properties, such as enhanced durability and corrosion resistance. The evolution of thermal properties in FRPCs is crucial for advancing thermal management systems, optimizing material performance, and enhancing energy efficiency across these diverse sectors. Despite significant research efforts to develop new materials with improved thermal properties and reduced thermal degradation, there is a lack of understanding of the thermal transport phenomena considering the influence of microscale reinforcement morphology in these composites. In the current study, we performed experimental investigations complemented by computations to determine the thermal transport properties and associated phenomena in epoxy and carbon fiber-reinforced epoxy composites. The experimental findings were utilized as input data for numerical analysis to examine the impact of fiber morphology and volume fraction in thermal transport phenomena. Our results revealed that composites incorporating non-circular fibers manifested higher thermal conductivity than traditional circular fibers in the transverse direction. This can be attributed to increased interconnected heat flow pathways facilitated by the increased surface area of non-circular fibers with the same cross-sectional areas, resulting in efficient heat transfer.

Let $L= - \mathrm{div} (A \nabla \cdot)$ be an elliptic operator defined on an open subset of $\mathbb{R}^d$, complemented with mixed boundary conditions. Under suitable assumptions on the operator and the geometry, we derive an atomic characterization (depending only on the boundary conditions) for the Hardy space $H^1_L$ defined using an adapted square function for $L$. This generalizes known results of Auscher and Russ in the case of pure Dirichlet/Neumann boundary conditions on Lipschitz domains. In particular, we develop a connection between the harmonic analysis of $L$ and its underlying geometry., Comment: 40 pages

Given an elliptic operator $L= - \mathrm{div} (A \nabla \cdot)$ subject to mixed boundary conditions on an open subset of $\mathbb{R}^d$, we study the relation between Gaussian pointwise estimates for the kernel of the associated heat semigroup, H\"older continuity of $L$-harmonic functions and the growth of the Dirichlet energy. To this end, we generalize an equivalence theorem of Auscher and Tchamitchian to the case of mixed boundary conditions and to open sets far beyond Lipschitz domains. Yet we prove consistency of our abstract result by encompassing operators with real-valued coefficients and their small complex perturbations into one of the aforementioned equivalent properties. The resulting kernel bounds open the door for developing a harmonic analysis for the associated semigroups on rough open sets., Comment: 44 pages, 3 figures, problem with enumeration of theorems, equations, etc. is fixed, Appendix B is added

We give a simple argument to obtain $\mathrm{L}^p$-boundedness for heat semigroups associated to uniformly strongly elliptic systems on $\mathbb{R}^d$ by using Stein interpolation between Gaussian estimates and hypercontractivity. Our results give $p$ explicitly in terms of ellipticity. It is optimal at the endpoint $p=\infty$. We also obtain $\mathrm{L}^p$-estimates for the gradient of the semigroup, where $p>2$ depends on ellipticity but not on dimension., Comment: 16 pages, improved readability, accepted for publication in Bulletin of the LMS

We numerically benchmark methods for computing harmonic maps into the unit sphere, with particular focus on harmonic maps with singularities. For the discretization we compare two different approaches, both based on Lagrange finite elements. While the first method enforces the unit-length constraint only at the Lagrange nodes, the other one adds a pointwise projection to fulfill the constraint everywhere. For the solution of the resulting algebraic problems we compare a nonconforming gradient flow with a Riemannian trust-region method. Both are energy-decreasing and can be shown to converge globally to a stationary point of the Dirichlet energy. We observe that while the nonconforming and the conforming discretizations both show similar behavior, the second-order trust-region method needs less iterations than the solver based on gradient flow.

The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium -- a property that makes such objects relevant for the fabrication of active and functional materials. In this paper we study microheterogeneous, prestrained plates that feature nonflat equilibrium shapes. Our goal is to understand the relation between the properties of the prestrained microstructure and the global shape of the plate in mechanical equilibrium. To this end, we consider a three-dimensional, nonlinear elasticity model that describes a periodic material that occupies a domain with small thickness. We consider a spatially periodic prestrain described in the form of a multiplicative decomposition of the deformation gradient. By simultaneous homogenization and dimension reduction, we rigorously derive an effective plate model as a {\Gamma}-limit for vanishing thickness and period. That limit has the form of a nonlinear bending energy with an emergent spontaneous curvature term. The homogenized properties of the bending model (bending stiffness and spontaneous curvature) are characterized by corrector problems. For a model composite -- a prestrained laminate composed of isotropic materials -- we investigate the dependence of the homogenized properties on the parameters of the model composite. Secondly, we investigate the relation between the parameters of the model composite and the set of shapes with minimal bending energy. Our study reveals a rather complex dependence of these shapes on the composite parameters., Comment: 79 pages, 21 figures

Advances in machine learning methods provide tools that have broad applicability in scientific research. These techniques are being applied across the diversity of nuclear physics research topics, leading to advances that will facilitate scientific discoveries and societal applications. This Review gives a snapshot of nuclear physics research which has been transformed by machine learning techniques., Comment: Comments are welcome

We summarize the ongoing scientific program of the 12 GeV Continuous Electron Beam Accelerator Facility (CEBAF) and give an outlook into future scientific opportunities. The program addresses important topics in nuclear, hadronic, and electroweak physics including nuclear femtography, meson and baryon spectroscopy, quarks and gluons in nuclei, precision tests of the standard model, and dark sector searches. Potential upgrades of CEBAF are considered, such as higher luminosity, polarized and unpolarized positron beams, and doubling the beam energy., Comment: To be published by Progress in Particle and Nuclear Physics in 2022

We describe an analysis comparing the $p\bar{p}$ elastic cross section as measured by the D0 Collaboration at a center-of-mass energy of 1.96 TeV to that in $pp$ collisions as measured by the TOTEM Collaboration at 2.76, 7, 8, and 13 TeV using a model-independent approach. The TOTEM cross sections extrapolated to a center-of-mass energy of $\sqrt{s} =$ 1.96 TeV are compared with the D0 measurement in the region of the diffractive minimum and the second maximum of the $pp$ cross section. The two data sets disagree at the 3.4$\sigma$ level and thus provide evidence for the $t$-channel exchange of a colorless, $C$-odd gluonic compound, also known as the odderon. We combine these results with a TOTEM analysis of the same $C$-odd exchange based on the total cross section and the ratio of the real to imaginary parts of the forward elastic scattering amplitude in $pp$ scattering. The combined significance of these results is larger than 5$\sigma$ and is interpreted as the first observation of the exchange of a colorless, $C$-odd gluonic compound., Comment: D0 and TOTEM Collaborations

This report is an outcome of the workshop "AI for Nuclear Physics" held at Thomas Jefferson National Accelerator Facility on March 4-6, 2020. The workshop brought together 184 scientists to explore opportunities for Nuclear Physics in the area of Artificial Intelligence. The workshop consisted of plenary talks, as well as six working groups. The report includes the workshop deliberations and additional contributions to describe prospects for using AI across Nuclear Physics research., Comment: This version includes reference updates, improved figures and minor clarifications in the text

In this chapter of the High Energy Physics Software Foundation Community Whitepaper, we discuss the current state of infrastructure, best practices, and ongoing developments in the area of data and software preservation in high energy physics. A re-framing of the motivation for preservation to enable re-use is presented. A series of research and development goals in software and other cyberinfrastructure that will aid in the enabling of reuse of particle physics analyses and production software are presented and discussed.

This paper describes the design and construction of the MicroBooNE liquid argon time projection chamber and associated systems. MicroBooNE is the first phase of the Short Baseline Neutrino program, located at Fermilab, and will utilize the capabilities of liquid argon detectors to examine a rich assortment of physics topics. In this document details of design specifications, assembly procedures, and acceptance tests are reported.