arXiv subjects

Brian Wynne

Publications and source records attributed to Brian Wynne.

7 recordsLinked to original sources

arXiv2026

Extension of a multi-region free-surface MHD solver beyond the inductionless approximation

Free-surface liquid metal flows are a leading candidate for the plasma-facing components of future fusion reactors, but existing transient, three-dimensional, free-surface MHD solvers rely on the inductionless approximation, in which the induced magnetic field is neglected. This paper extends the open-source solver FreeMHD [B. Wynne et al., Phys. Plasmas 32, 013907 (2025)] beyond that approximation, resolving the induced field self-consistently with a vector-potential formulation that enforces $\nabla\cdot\boldsymbol{B}=0$ by construction while preserving the original multi-region, two-phase framework. It is verified against the analytical Shercliff and Hunt duct flows, against flows driven by a time-varying applied field, and against the deformation of a free liquid metal jet crossing a non-uniform field, and validated against free-surface height measurements from the LMX-U experiment. The experiment validates the overall free-surface solution rather than finite-$R_m$ effects, which the transient-field cases verify. To our knowledge this is the first open-source, fully three-dimensional free-surface liquid metal solver to resolve the evolution of the induced magnetic field, providing a basis for modeling the finite magnetic Reynolds number conditions expected in large-scale, transient fusion events.

physics.comp-ph↗

arXiv2026

Semi-boolean and Yosida $\ell$-groups, Martinez and Yosida frames, and the $G+B$ construction

The class of semi-boolean $\ell$-groups was introduced in 1968 by A. Bigard. These are the $\ell$-groups $G$ in which the principal convex $\ell$-subgroup $G(a)$ generated by any $a \in G$ is equal to the polar $a^{\perp \perp}$. Examples include all hyperarchimedean $\ell$-groups and all existentially closed abelian $\ell$-groups. Ordered by inclusion, the set of convex $\ell$-subgroups of a semi-boolean $\ell$-group is a \Mart frame (an algebraic frame with FIP in which every element is a $d$-element). Related are the Yosida $\ell$-groups, i.e., the $\ell$-groups whose frame of convex $\ell$-subgroups is a Yosida frame (an algebraic frame with FIP in which every compact element is a meet of maximal elements). Applying results on \Mart frames and Yosida frames, we obtain new characterizations of the semi-boolean and Yosida $\ell$-groups, show that the former constitute a radical class and the latter do not, and present new examples with special properties. To build some of our examples, we introduce the $G+B$ construction for $\ell$-groups, an adaptation of the $A+B$ construction from commutative algebra.

math.GR↗

arXiv2025

One-shot acceleration of transient PDE solvers via online-learned preconditioners

Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications. The focus thus far has been on methods that require classical simulations to train, which when combined with the data-hungriness and optimization challenges of neural networks has caused difficulties in demonstrating a convincing advantage against strong classical baselines. We consider an alternative paradigm in which the learner uses a classical solver's own data to accelerate it, enabling a one-shot speedup of the simulation. Concretely, since transient PDEs often require solving a sequence of related linear systems, the feedback from repeated calls to a linear solver such as preconditioned conjugate gradient (PCG) can be used by a bandit algorithm to online-learn an adaptive sequence of solver configurations (e.g. preconditioners). The method we develop, PCGBandit, is implemented directly on top of the popular open-source software OpenFOAM, which we use to show its effectiveness on a set of fluid and magnetohydrodynamics (MHD) problems.

physics.comp-ph↗

arXiv2024

FreeMHD: validation and verification of the open-source, multi-domain, multi-phase solver for electrically conductive flows

The extreme heat fluxes in the divertor region of tokamaks may require an alternative to solid plasma-facing components, for the extraction of heat and the protection of the surrounding walls. Flowing liquid metals are proposed as an alternative, but raise additional challenges that require investigation and numerical simulations. Free surface designs are desirable for plasma-facing components (PFCs), but steady flow profiles and surface stability must be ensured to limit undesirable interactions with the plasma. Previous studies have mainly used steady-state, 2D, or simplified models for internal flows and have not been able to adequately model free-surface liquid metal (LM) experiments. Therefore, FreeMHD has been recently developed as an open-source magnetohydrodynamics (MHD) solver for free-surface electrically conductive flows subject to a strong external magnetic field. The FreeMHD solver computes incompressible free-surface flows with multi-region coupling for the investigation of MHD phenomena involving fluid and solid domains. The model utilizes the finite-volume OpenFOAM framework under the low magnetic Reynolds number approximation. FreeMHD is validated using analytical solutions for the velocity profiles of closed channel flows with various Hartmann numbers and wall conductance ratios. Next, experimental measurements are then used to verify FreeMHD, through a series of cases involving dam breaking, 3D magnetic fields, and free-surface LM flows. These results demonstrate that FreeMHD is a reliable tool for the design of LM systems under free surface conditions at the reactor scale. Furthermore, it is flexible, computationally inexpensive, and can be used to solve fully 3D transient MHD flows.

physics.plasm-ph↗

arXiv2024

Archimedean l-groups with strong unit: cozero-sets and coincidence of types of ideals

$\bf{W}^*$ is the category of the archimedean l-groups with distinguished strong order unit and unit-preserving l-group homomorphisms. For $G \in \bf{W}^*$, we have the canonical compact space $YG$, and Yosida representation $G \leq C(YG)$, thus, for $g \in G$, the cozero-set coz(g) in $YG$. The ideals at issue in $G$ include the principal ideals and polars, $G(g)$ and $g^{\perp \perp}$, respectively, and the $\bf{W}^*$-kernels of $\bf{W}^*$-morphisms from $G$. The ``coincidences of types" include these properties of $G$: (M) Each $G(g) = g^{\perp \perp}$; (Y) Each $G(g)$ is a $\bf{W}^*$-kernel; (CR) Each $g^{\perp \perp}$ is a $\bf{W}^*$-kernel (iff each coz(g) is regular open). For each of these, we give numerous ``rephrasings", and examples, and note that (M) = (Y) $\cap$ (CR). This paper is a companion to a paper in preparation by the present authors, which includes the present thrust in contexts less restrictive and more algebraic. Here, the focus on $\bf{W}^*$ brings topology to bear, and sharpens the view.

math.GR↗

arXiv2024

Sufficiently many projections in archimedean vector lattices with weak order unit

The property of a vector lattice of sufficiently many projections (SMP) is informed by restricting attention to archimedean $A$ with a distinguished weak order unit $u$ (the class, or category, $\bf{W}$), where the Yosida representation $A \leq D(Y(A,u))$ is available. Here, $A$ SMP is equivalent to $Y(A,u)$ having a $π$-base of clopen sets of a certain type called ``local". If the unit is strong, all clopen sets are local and $A$ is SMP if and only if $Y(A,u)$ has clopen $π$-base, a property we call $π$-zero-dimensional ($π$ZD). The paper is in two parts: the first explicates the similarities of SMP and $π$ZD; the second consists of examples, including $π$ZD but not SMP, and constructions of many SMP's which seem scarce in the literature.

math.GN↗

arXiv2022

Defect engineering of silicon with ion pulses from laser acceleration

Defect engineering is foundational to classical electronic device development and for emerging quantum devices. Here, we report on defect engineering of silicon single crystals with ion pulses from a laser accelerator with ion flux levels up to 10^22 ions/cm^2/s. Low energy ions from plasma expansion of the laser-foil target are implanted near the surface and then diffuse into silicon samples that were locally pre-heated by high energy ions. We observe low energy ion fluences of ~10^16 cm^-2, about four orders of magnitude higher than the fluence of high energy (MeV) ions. In the areas of highest energy deposition, silicon crystals exfoliate from single ion pulses. Color centers, predominantly W and G-centers, form directly in response to ion pulses without a subsequent annealing step. We find that the linewidth of G-centers increase in areas with high ion flux much more than the linewidth of W-centers, consistent with density functional theory calculations of their electronic structure. Laser ion acceleration generates aligned pulses of high and low energy ions that expand the parameter range for defect engineering and doping of semiconductors with tunable balances of ion flux, damage rates and local heating.

cond-mat.mtrl-sci↗