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Mark K. Transtrum

Publications and source records attributed to Mark K. Transtrum.

At least 37 records · Page 2Linked to original sources
arXiv2020

Analysis of Magnetic Vortex Dissipation in Sn-Segregated Boundaries in Nb$_3$Sn Superconducting RF Cavities

We study mechanisms of vortex nucleation in Nb$_3$Sn Superconducting RF (SRF) cavities using a combination of experimental, theoretical, and computational methods. Scanning transmission electron microscopy (STEM) image and energy dispersive spectroscopy (EDS) of some Nb$_3$Sn cavities show Sn segregation at grain boundaries in Nb$_3$Sn with Sn concentration as high as $\sim$35 at.\% and widths $\sim$3 nm in chemical composition. Using ab initio calculations, we estimate the effect excess tin has on the local superconducting properties of the material. We model Sn segregation as a lowering of the local critical temperature. We then use time-dependent Ginzburg-Landau theory to understand the role of segregation on magnetic vortex nucleation. Our simulations indicate that the grain boundaries act as both nucleation sites for vortex penetration and pinning sites for vortices after nucleation. Depending on the magnitude of the applied field, vortices may remain pinned in the grain boundary or penetrate the grain itself. We estimate the superconducting losses due to vortices filling grain boundaries and compare with observed performance degradation with higher magnetic fields. We estimate that the quality factor may decrease by an order of magnitude ($10^{10}$ to $10^9$) at typical operating fields if 0.03\% of the grain boundaries actively nucleate vortices. We additionally estimate the volume that would need to be filled with vortices to match experimental observations of cavity heating.

cond-mat.supr-con↗
arXiv2020

Role of surface defects and material inhomogeneities for vortex nucleation in superconductors within time-dependent Ginzburg-Landau theory in 2 and 3 dimensions

We use Time-Dependent Ginzburg-Landau theory to study the nucleation of vortices in type II superconductors in the presence of both geometric and material inhomogeneities. The superconducting Meissner state is meta-stable up to a critical magnetic field, known as the superheating field. For a uniform surface and homogenous material, the superheating transition is driven by a non-local critical mode in which an array of vortices simultaneously penetrate the surface. In contrast, we show that even a small amount of disorder localizes the critical mode and can have a significant reduction in the effective superheating field for a particular sample. Vortices can be nucleated by either surface roughness or local variations in material parameters, such as Tc. Our approach uses a finite element method to simulate a cylindrical geometry in 2 dimensions and a film geometry in 2 and 3 dimensions. We combine saddle node bifurcation analysis along with a novel fitting procedure to evaluate the superheating field and identify the unstable mode. We demonstrate agreement with previous results for homogenous geometries and surface roughness and extend the analysis to include variations in material properties. Finally, we show that in three dimensions, suface divots not aligned with the applied field can increase the super heating field. We discuss implications for fabrication and performance of superconducting resonant frequency cavities in particle accelerators.

physics.comp-ph↗
arXiv2019

$\textit{Ab Initio}$ Study of Antisite Defects in Nb$_3$Sn: Phase Diagram and Impact on Superconductivity

Antisite defects play a critical role in Nb$_3$Sn superconducting radio frequency (SRF) cavity physics. Such defects are the primary form of disorder in Nb$_3$Sn, and are responsible for stoichiometry variations, including experimentally observed tin-depleted regions within grains and tin-rich regions around grain boundaries. But why they cluster to form regions of different stoichiometries and how they affect the SRF properties of Nb$_3$Sn cavities are not fully understood. Using $\textit{ab initio}$ techniques, we calculate the A15 region of the Nb-Sn phase diagram, discuss a possible modification to the phase diagram near grain boundaries, and calculate $T_c$ as a function of stoichiometry, including experimentally inaccessible tin-rich stoichiometry. We find that the impact of antisite defects on the density of states near the Fermi-level of Nb$_3$Sn plays a key role in determining many of their properties. These results improve our understanding of the obstacles facing Nb$_3$Sn SRF systems, and how modified growth processes might overcome them.

cond-mat.supr-con↗
arXiv2019

Unwinding the model manifold: choosing similarity measures to remove local minima in sloppy dynamical systems

In this paper, we consider the problem of parameter sensitivity in models of complex dynamical systems through the lens of information geometry. We calculate the sensitivity of model behavior to variations in parameters. In most cases, models are sloppy, that is, exhibit an exponential hierarchy of parameter sensitivities. We propose a parameter classification scheme based on how the sensitivities scale at long observation times. We show that for oscillatory models, either with a limit cycle or a strange attractor, sensitivities can become arbitrarily large, which implies a high effective-dimensionality on the model manifold. Sloppy models with a single fixed point have model manifolds with low effective-dimensionality, previously described as a "hyper-ribbon". In contrast, models with high effective dimensionality translate into multimodal fitting problems. We define a measure of curvature on the model manifold which we call the \emph{winding frequency} that estimates the linear density of local minima in the model's parameter space. We then show how alternative choices of fitting metrics can "unwind" the model manifold and give low winding frequencies. This prescription translates the model manifold from one of high effective-dimensionality into the "hyper-ribbon" structures observed elsewhere. This translation opens the door for applications of sloppy model analysis and model reduction methods developed for models with low effective-dimensionality.

cond-mat.stat-mech↗
arXiv2019

Model Boundary Approximation Method as a Unifying Framework for Balanced Truncation and Singular Perturbation Approximation

We show that two widely accepted model reduction techniques, Balanced Truncation and Balanced Singular Perturbation Approximation, can be derived as limiting approximations of a carefully constructed parameterization of Linear Time Invariant (LTI) systems by employing the Model Boundary Approximation Method (MBAM), a recent development in the Physics literature. This unifying framework of these popular model reduction techniques shows that Balanced Truncation and Balanced Singular Perturbation Approximation each correspond to a particular boundary point on a manifold, the "model manifold," which is associated with the specific choice of model parameterization and initial condition, and is embedded in a sample space of measured outputs, which can be chosen arbitrarily, provided that the number of samples exceeds the number of parameters. We also show that MBAM provides a novel way to interpolate between Balanced Truncation and Balanced Singular Perturbation Approximation, by exploring the set of approximations on the boundary of the manifold between the elements that correspond to the two model reduction techniques; this allows for alternative approximations of a given system to be found that may be better under certain conditions. The work herein suggests similar types of approximations may be obtainable in topologically similar places (i.e. on certain boundaries) on the model manifold of nonlinear systems if analogous parameterizations can be achieved, therefore extending these widely accepted model reduction techniques to nonlinear systems.

math.OC↗
arXiv2018

Maximizing the information learned from finite data selects a simple model

We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as much as possible from limited data. When many parameters are poorly constrained by the available data, we find that this prior puts weight only on boundaries of the parameter manifold. Thus it selects a lower-dimensional effective theory in a principled way, ignoring irrelevant parameter directions. In the limit where there is sufficient data to tightly constrain any number of parameters, this reduces to Jeffreys prior. But we argue that this limit is pathological when applied to the hyper-ribbon parameter manifolds generic in science, because it leads to dramatic dependence on effects invisible to experiment.

physics.data-an↗
arXiv2018

The Spectrum of Mechanism-oriented Models for Explanations of Biological Phenomena

Within the diverse interdisciplinary life sciences domains, semantic, workflow, and methodological ambiguities can prevent the appreciation of explanations of phenomena, handicap the use of computational models, and hamper communication among scientists, engineers, and the public. Members of the life sciences community commonly, and too often loosely, draw on "mechanistic model" and similar phrases when referring to the processes of discovering and establishing causal explanations of biological phenomena. Ambiguities in modeling and simulation terminology and methods diminish clarity, credibility, and the perceived significance of research findings. To encourage improved semantic and methodological clarity, we describe the spectrum of Mechanism-oriented Models being used to develop explanations of biological phenomena. We cluster them into three broad groups. We then expand the three groups into a total of seven workflow-related model types having clearly distinguishable features. We name each type and illustrate with diverse examples drawn from the literature. These model types are intended to contribute to the foundation of an ontology of mechanism-based simulation research in the life sciences. We show that it is within the model-development workflows that the different model types manifest and exert their scientific usefulness by enhancing and extending different forms and degrees of explanation. The process starts with knowledge about the phenomenon and continues with explanatory and mathematical descriptions. Those descriptions are transformed into software and used to perform experimental explorations by running and examining simulation output. The credibility of inferences is thus linked to having easy access to the scientific and technical provenance from each workflow stage.

q-bio.QM↗
arXiv2017

SRF Theory Developments from the Center for Bright Beams

We present theoretical studies of SRF materials from the Center for Bright Beams. First, we discuss the effects of disorder, inhomogeneities, and materials anisotropy on the maximum parallel surface field that a superconductor can sustain in an SRF cavity, using linear stability in conjunction with Ginzburg-Landau and Eilenberger theory. We connect our disorder mediated vortex nucleation model to current experimental developments of Nb$_3$Sn and other cavity materials. Second, we use time-dependent Ginzburg-Landau simulations to explore the role of inhomogeneities in nucleating vortices, and discuss the effects of trapped magnetic flux on the residual resistance of weakly- pinned Nb$_3$Sn cavities. Third, we present first-principles density-functional theory (DFT) calculations to uncover and characterize the key fundamental materials processes underlying the growth of Nb$_3$Sn. Our calculations give us key information about how, where, and when the observed tin-depletedregions form. Based on this we plan to develop new coating protocols to mitigate the formation of tin depleted regions.

physics.acc-ph↗
arXiv2016

Theoretical estimates of maximum fields in superconducting resonant radio frequency cavities: Stability theory, disorder, and laminates

Theoretical limits to the performance of superconductors in high magnetic fields parallel to their surfaces are of key relevance to current and future accelerating cavities, especially those made of new higher-Tc materials such as Nb$_3$Sn, NbN, and MgB$_2$. Indeed, beyond the so-called superheating field $H_{\mathcal{sh}}$, flux will spontaneously penetrate even a perfect superconducting surface and ruin the performance. We present intuitive arguments and simple estimates for $H_{\mathcal{sh}}$, and combine them with our previous rigorous calculations, which we summarize. We briefly discuss experimental measurements of the superheating field, comparing to our estimates. We explore the effects of materials anisotropy and the danger of disorder in nucleating vortex entry. Will we need to control surface orientation in the layered compound MgB$_2$? Can we estimate theoretically whether dirt and defects make these new materials fundamentally more challenging to optimize than niobium? Finally, we discuss and analyze recent proposals to use thin superconducting layers or laminates to enhance the performance of superconducting cavities. Flux entering a laminate can lead to so-called pancake vortices; we consider the physics of the dislocation motion and potential re-annihilation or stabilization of these vortices after their entry.

cond-mat.supr-con↗
arXiv2016

Ginzburg-Landau theory of the superheating field anisotropy of layered superconductors

We investigate the effects of material anisotropy on the superheating field of layered superconductors. We provide an intuitive argument both for the existence of a superheating field, and its dependence on anisotropy, for $κ= λ/ ξ$ (the ratio of magnetic to superconducting healing lengths) both large and small. On the one hand, the combination of our estimates with published results using a two-gap model for MgB${}_2$ suggests high anisotropy of the superheating field near zero temperature. On the other hand, within Ginzburg-Landau theory for a single gap, we see that the superheating field shows significant anisotropy only when the crystal anisotropy is large and the Ginzburg-Landau parameter $κ$ is small. We then conclude that only small anisotropies in the superheating field are expected for typical unconventional superconductors near the critical temperature. Using a generalized form of Ginzburg Landau theory, we do a quantitative calculation for the anisotropic superheating field by mapping the problem to the isotropic case, and present a phase diagram in terms of anisotropy and $κ$, showing type I, type II, or mixed behavior (within Ginzburg-Landau theory), and regions where each asymptotic solution is expected. We estimate anisotropies for a number of different materials, and discuss the importance of these results for radio-frequency cavities for particle accelerators.

cond-mat.supr-con↗
arXiv2016

Information topology identifies emergent model classes

We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived. Using Information Geometry, we consider geometric properties of statistical models for different observations. As observations are varied, the model manifold may be stretched, compressed, or even collapsed. Observations that preserve the structural identifiability of the parameters also preserve certain topological features (such as edges and corners) that characterize the model's underlying physical principles. We introduce Information Topology in analogy with information geometry as characterizing the "abstract model" of which statistical models are realizations. Observations that change the topology, i.e., "manifold collapse," require a modification of the abstract model in order to construct identifiable statistical models. Often, the essential topological feature is a hierarchical structure of boundaries (faces, edges, corners, etc.) which we represent as a hierarchical graph known as a Hasse diagram. Low-dimensional elements of this diagram are simple models that describe the dominant behavioral modes, what we call emergent model classes. Observations that preserve the Hasse diagram are diffeomorphically related and form a group, the collection of which form a partially ordered set. All possible observations have a semi-group structure. For hierarchical models, we consider how the topology of simple models is embedded in that of larger models. When emergent model classes are unstable to the introduction of new parameters, we classify the new parameters as relevant. Conversely, the emergent model classes are stable to the introduction of irrelevant parameters. In this way, information topology provides a general language for exploring representations of physical systems and their relationships to observations.

physics.data-an↗
arXiv2016

The limitations of model-based experimental design and parameter estimation in sloppy systems

We explore the relationship among model fidelity, experimental design, and parameter estimation in sloppy models. We show that the approximate nature of mathematical models poses challenges for experimental design in sloppy models. In many models of complex biological processes it is unknown what are the relevant physics that must be included to explain collective behaviors. As a consequence, models are often overly complex, with many practically unidentifiable parameters. Furthermore, which details are relevant/irrelevant vary among potential experiments. By selecting complementary experiments, experimental design may inadvertently make details that were ommitted from the model become relevant. When this occurs, the model will fail to give a good fit to the data. We use a simple hyper-model of model error to quantify a model's inadequacy and apply it to two models of complex biological processes (EGFR signaling and DNA repair) with optimally selected experiments. We find that although parameters may be accurately estimated, the error in the model renders it less predictive than it was in the sloppy regime where model error is small. We introduce the concept of a \emph{sloppy system}--a sequence of models of increasing complexity that become sloppy in the limit of microscopic accuracy. We explore the limits of accurate parameter estimation in sloppy systems and argue that system identification better approached by considering a hierarchy of models of varying detail rather than focusing parameter estimation in a single model.

q-bio.QM↗
arXiv2016

Manifold boundaries give "gray-box" approximations of complex models

We discuss a method of parameter reduction in complex models known as the Manifold Boundary Approximation Method (MBAM). This approach, based on a geometric interpretation of statistics, maps the model reduction problem to a geometric approximation problem. It operates iteratively, removing one parameter at a time, by approximating a high-dimension, but thin manifold by its boundary. Although the method makes no explicit assumption about the functional form of the model, it does require that the model manifold exhibit a hierarchy of boundaries, i.e., faces, edges, corners, hyper-corners, etc. We empirically show that a variety of model classes have this curious feature, making them amenable to MBAM. These model classes include models composed of elementary functions (e.g., rational functions, exponentials, and partition functions), a variety of dynamical system (e.g., chemical and biochemical kinetics, Linear Time Invariant (LTI) systems, and compartment models), network models (e.g., Bayesian networks, Markov chains, artificial neural networks, and Markov random fields), log-linear probability distributions, and models with symmetries. We discuss how MBAM recovers many common approximation methods for each model class and discuss potential pitfalls and limitations.

physics.data-an↗
arXiv2016

Bridging Mechanistic and Phenomenological Models of Complex Biological Systems

The inherent complexity of biological systems gives rise to complicated mechanistic models with a large number of parameters. On the other hand, the collective behavior of these systems can often be characterized by a relatively small number of phenomenological parameters. We use the Manifold Boundary Approximation Method (MBAM) as a tool for deriving simple phenomenological models from complicated mechanistic models. The resulting models are not black boxes, but remain expressed in terms of the microscopic parameters. In this way, we explicitly connect the macroscopic and microscopic descriptions, characterize the equivalence class of distinct systems exhibiting the same range of collective behavior, and identify the combinations of components that function as tunable control knobs for the behavior. We demonstrate the procedure for adaptation behavior exhibited by the EGFR pathway. From a 48 parameter mechanistic model, the system can be effectively described by a single adaptation parameter $τ$ characterizing the ratio of time scales for the initial response and recovery time of the system which can in turn be expressed as a combination of microscopic reaction rates, Michaelis-Menten constants, and biochemical concentrations. The situation is not unlike modeling in physics in which microscopically complex processes can often be renormalized into simple phenomenological models with only a few effective parameters. The proposed method additionally provides a mechanistic explanation for non-universal features of the behavior.

q-bio.QM↗
arXiv2015

Shielding superconductors with thin films

Determining the optimal arrangement of superconducting layers to withstand large amplitude AC magnetic fields is important for certain applications such as superconducting radiofrequency cavities. In this paper, we evaluate the shielding potential of the superconducting film/insulating film/superconductor (SIS') structure, a configuration that could provide benefits in screening large AC magnetic fields. After establishing that for high frequency magnetic fields, flux penetration must be avoided, the superheating field of the structure is calculated in the London limit both numerically and, for thin films, analytically. For intermediate film thicknesses and realistic material parameters we also solve numerically the Ginzburg-Landau equations. It is shown that a small enhancement of the superheating field is possible, on the order of a few percent, for the SIS' structure relative to a bulk superconductor of the film material, if the materials and thicknesses are chosen appropriately.

physics.acc-ph↗
arXiv2015

Sloppiness and Emergent Theories in Physics, Biology, and Beyond

Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are `sloppy', i.e., exhibit behavior controlled by a relatively small number of parameter combinations. We review an information theoretic framework for analyzing sloppy models. This formalism is based on the Fisher Information Matrix, which we interpret as a Riemannian metric on a parameterized space of models. Distance in this space is a measure of how distinguishable two models are based on their predictions. Sloppy model manifolds are bounded with a hierarchy of widths and extrinsic curvatures. We show how the manifold boundary approximation can extract the simple, hidden theory from complicated sloppy models. We attribute the success of simple effective models in physics as likewise emerging from complicated processes exhibiting a low effective dimensionality. We discuss the ramifications and consequences of sloppy models for biochemistry and science more generally. We suggest that the reason our complex world is understandable is due to the same fundamental reason: simple theories of macroscopic behavior are hidden inside complicated microscopic processes.

cond-mat.stat-mech↗
arXiv2013

Theoretical Field Limits for Multi-Layer Superconductors

The SIS structure---a thin superconducting film on a bulk superconductor separated by a thin insulating film---was propsed as a method to protect alternative SRF materials from flux penetration by enhancing the first critical field $B_{c1}$. In this work, we show that in fact $B_{c1}$ = 0 for a SIS structure. We calculate the superheating field $B_{sh}$, and we show that it can be enhanced slightly using the SIS structure, but only for a small range of film thicknesses and only if the film and the bulk are different materials. We also show that using a multilayer instead of a single thick layer is detrimental, as this decreases $B_{sh}$ of the film. We calculate the dissipation due to vortex penetration above the $B_{sh}$ of the film, and find that it is unmanageable for SRF applications. However, we find that if a gradient in the phase of the order parameter is introduced, SIS structures may be able to shield large DC and low frequency fields. We argue that the SIS structure is not beneficial for SRF cavities, but due to recent experiments showing low-surface-resistance performance above $B_{c1}$ in cavities made of superconductors with small coherence lengths, we argue that enhancement of $B_{c1}$ is not necessary, and that bulk films of alternative materials show great promise.

physics.acc-ph↗