arXiv subjects

James P. Sethna

Publications and source records attributed to James P. Sethna.

At least 55 records · Page 3Linked to original sources

arXiv2018

Vortex dynamics and losses due to pinning: Dissipation from trapped magnetic flux in resonant superconducting radio-frequency cavities

We use a model of vortex dynamics and collective weak pinning theory to study the residual dissipation due to trapped magnetic flux in a dirty superconductor. Using simple estimates, approximate analytical calculations, and numerical simulations, we make predictions and comparisons with experiments performed in CERN and Cornell on resonant superconducting radio-frequency NbCu, doped-Nb and Nb$_3$Sn cavities. We invoke hysteretic losses originating in a rugged pinning potential landscape to explain the linear behavior of the sensitivity of the residual resistance to trapped magnetic flux as a function of the amplitude of the radio-frequency field. Our calculations also predict and describe the crossover from hysteretic-dominated to viscous-dominated regimes of dissipation. We propose simple formulas describing power losses and crossover behavior, which can be used to guide the tuning of material parameters to optimize cavity performance.

cond-mat.supr-con↗

arXiv2018

Chebyshev approximation and the global geometry of sloppy models

Sloppy models are complex nonlinear models with outcomes that are significantly affected by only a small subset of parameter combinations. Despite forming an important universality class and arising frequently in practice, formal and systematic explanations of sloppiness are lacking. By unifying geometric interpretations of sloppiness with Chebyshev approximation theory, we offer such an explanation, and show how sloppiness can be described explicitly in terms of model smoothness. Our approach results in universal bounds on model predictions for classes of smooth models, and our bounds capture global geometric features that are intrinsic to their model manifolds. We illustrate these ideas using three disparate models: exponential decay, reaction rates from an enzyme-catalysed chemical reaction, and an epidemiology model of an infected population.

math.NA↗

arXiv2018

Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class

A replica-symmetry-breaking phase transition is predicted in a host of disordered media. The criticality of the transition has, however, long been questioned below its upper critical dimension, six, due to the absence of a critical fixed point in the renormalization-group flows at one-loop order. A recent two-loop analysis revealed a possible strong-coupling fixed point but, given the uncontrolled nature of perturbative analysis in the strong-coupling regime, debate persists. Here we examine the nature of the transition as a function of spatial dimension and show that the strong-coupling fixed point can go through a Hopf bifurcation, resulting in a critical limit cycle and a concomitant discrete scale invariance. We further investigate a different renormalization scheme and argue that the basin of attraction of the strong-coupling fixed point/limit cycle may thus stay finite for all dimensions.

cond-mat.stat-mech↗

arXiv2018

Computation of a Theoretical Membrane Phase Diagram, and the Role of Phase in Lipid Raft-Mediated Protein Organization

Lipid phase heterogeneity in the plasma membrane is thought to be crucial for many aspects of cell signaling, but the physical basis of participating membrane domains such as "lipid rafts" remains controversial. Here we consider a lattice model yielding a phase diagram that includes several states proposed to be relevant for the cell membrane, including microemulsion - which can be related to membrane curvature - and Ising critical behavior. Using a neural network-based machine learning approach, we compute the full phase diagram of this lattice model. We analyze selected regions of this phase diagram in the context of a signaling initiation event in mast cells: recruitment of the membrane-anchored tyrosine kinase Lyn to a cluster of transmembrane of IgE-FcεRI receptors. We find that model membrane systems in microemulsion and Ising critical states can mediate roughly equal levels of kinase recruitment (binding energy ~ -0.6 kBT), whereas a membrane near a tricritical point can mediate much stronger kinase recruitment (-1.7 kBT). By comparing several models for lipid heterogeneity within a single theoretical framework, this work points to testable differences between existing models. We also suggest the tricritical point as a new possibility for the basis of membrane domains that facilitate preferential partitioning of signaling components.

physics.bio-ph↗

arXiv2018

Canonical Sectors and Evolution of Firms in the US Stock Markets

A classification of companies into sectors of the economy is important for macroeconomic analysis and for investments into the sector-specific financial indices and exchange traded funds (ETFs). Major industrial classification systems and financial indices have historically been based on expert opinion and developed manually. Here we show how unsupervised machine learning can provide a more objective and comprehensive broad-level sector decomposition of stocks. An emergent low-dimensional structure in the space of historical stock price returns automatically identifies "canonical sectors" in the market, and assigns every stock a participation weight into these sectors. Furthermore, by analyzing data from different periods, we show how these weights for listed firms have evolved over time.

q-fin.ST↗

arXiv2017

Visualizing theory space: Isometric embedding of probabilistic predictions, from the Ising model to the cosmic microwave background

We develop an intensive embedding for visualizing the space of all predictions for probabalistic models, using replica theory. Our embedding is isometric (preserves the distinguishability between models) and faithful (yields low-dimensional visualizations of models with simple emergent behavior). We apply our intensive embedding to the Ising model of statistical mechanics and the $Λ$CDM model applied to cosmic microwave background radiation. It provides an intuitive, quantitative visualization applicable to renormalization-group calculations and optimal experimental design.

cond-mat.stat-mech↗

arXiv2017

Finding stability domains and escape rates in kicked Hamiltonians

We use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the resonances, the dynamics typically has a finite region in phase space where it is stable. Inherent noise in the system leads to particle loss from this stable region. The competition of this noise with radiation damping, which increases stability, determines the escape rate. Determining this `aperture' and finding escape rates is therefore an important physical problem. We compare the results of two different perturbation theories and a variational method to estimate this stable region. Including noise, we derive analytical estimates for the steady-state populations (and the resulting beam emittance), for the escape rate in the small damping regime, and compare them with numerical simulations.

cond-mat.stat-mech↗

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↗

arXiv2017

Jeffrey's prior sampling of deep sigmoidal networks

Neural networks have been shown to have a remarkable ability to uncover low dimensional structure in data: the space of possible reconstructed images form a reduced model manifold in image space. We explore this idea directly by analyzing the manifold learned by Deep Belief Networks and Stacked Denoising Autoencoders using Monte Carlo sampling. The model manifold forms an only slightly elongated hyperball with actual reconstructed data appearing predominantly on the boundaries of the manifold. In connection with the results we present, we discuss problems of sampling high-dimensional manifolds as well as recent work [M. Transtrum, G. Hart, and P. Qiu, Submitted (2014)] discussing the relation between high dimensional geometry and model reduction.

cond-mat.dis-nn↗

arXiv2017

Using Sloppy Models for Constrained Emittance Minimization at the Cornell Electron Storage Ring (CESR)

In order to minimize the emittance at the Cornell Electron Storage Ring (CESR), we measure and correct the orbit, dispersion, and transverse coupling of the beam. However, this method is limited by finite measurement resolution of the dispersion, and so a new procedure must be used to further reduce the emittance due to dispersion. In order to achieve this, we use a method based upon the theory of sloppy models. We use a model of the accelerator to create the Hessian matrix which encodes the effects of various corrector magnets on the vertical emittance. A singular value decomposition of this matrix yields the magnet combinations which have the greatest effect on the emittance. We can then adjust these magnet "knobs" sequentially in order to decrease the dispersion and the emittance. We present here comparisons of the effectiveness of this procedure in both experiment and simulation using a variety of CESR lattices. We also discuss techniques to minimize changes to parameters we have already corrected.

physics.acc-ph↗

arXiv2017

Emergent SO(3) Symmetry of the Frictionless Shear Jamming Transition

We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. Despite these striking differences, we argue that in a deeper sense, the shear jamming and isotropic jamming transitions actually have the same symmetry, and that the differences can be fully understood by rotating the six-dimensional basis of the elastic modulus tensor.

cond-mat.soft↗

arXiv2017

Light Microscopy at Maximal Precision

Microscopy is the workhorse of the physical and life sciences, producing crisp images of everything from atoms to cells well beyond the capabilities of the human eye. However, the analysis of these images is frequently little better than automated manual marking. Here, we revolutionize the analysis of microscopy images, extracting all the information theoretically contained in a complex microscope image. Using a generic, methodological approach, we extract the information by fitting experimental images with a detailed optical model of the microscope, a method we call Parameter Extraction from Reconstructing Images (PERI). As a proof of principle, we demonstrate this approach with a confocal image of colloidal spheres, improving measurements of particle positions and radii by 100x over current methods and attaining the maximum possible accuracy. With this unprecedented resolution, we measure nanometer-scale colloidal interactions in dense suspensions solely with light microscopy, a previously impossible feat. Our approach is generic and applicable to imaging methods from brightfield to electron microscopy, where we expect accuracies of 1 nm and 0.1 pm, respectively.

cond-mat.soft↗

arXiv2016

Deformation of crystals: Connections with statistical physics

We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, and a broad introduction into the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in magnets, spin glasses, charge density waves, and dilute colloidal suspensions are discussed in relation to the onset of plastic yielding in crystals. Dislocation avalanches and complex dislocation tangles are discussed via a brief introduction to the renormalization group and scaling. Analogies to emergent scale invariance in fracture, jamming, coarsening, and a variety of depinning transitions are explored. Dislocation dynamics in crystals challenges non equilibrium statistical physics. Statistical physics provides both cautionary tales of subtle memory effects in nonequilibrium systems, and systematic tools designed to address complex scale-invariant behavior on multiple length and time scales.

cond-mat.mtrl-sci↗

arXiv2016

A KIM-compliant potfit for fitting sloppy interatomic potentials: Application to the EDIP model for silicon

Fitted interatomic potentials are widely used in atomistic simulations thanks to their ability to compute the energy and forces on atoms quickly. However, the simulation results crucially depend on the quality of the potential being used. Force matching is a method aimed at constructing reliable and transferable interatomic potentials by matching the forces computed by the potential as closely as possible, with those obtained from first principles calculations. The potfit program is an implementation of the force-matching method that optimizes the potential parameters using a global minimization algorithm followed by a local minimization polish. We extended potfit in two ways. First, we adapted the code to be compliant with the KIM Application Programming Interface (API) standard (part of the Knowledgebase of Interatomic Models Project). This makes it possible to use potfit to fit many KIM potential models, not just those prebuilt into the potfit code. Second, we incorporated the geodesic Levenberg--Marquardt (LM) minimization algorithm into potfit as a new local minimization algorithm. The extended potfit was tested by generating a training set using the KIM Environment-Dependent Interatomic Potential (EDIP) model for silicon and using potfit to recover the potential parameters from different initial guesses. The results show that EDIP is a "sloppy model" in the sense that its predictions are insensitive to some of its parameters, which makes fitting more difficult. We find that the geodesic LM algorithm is particularly efficient for this case. The extended potfit code is the first step in developing a KIM-based fitting framework for interatomic potentials for bulk and two dimensional materials. The code is available for download via https://www.potfit.net.

cond-mat.other↗

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

Measuring nonlinear stresses generated by defects in 3D colloidal crystals

The mechanical, structural and functional properties of crystals are determined by their defects and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect density rises to levels routinely found in real-world materials, transport is governed by local stresses that are predominantly nonlinear. Such stress fields however, cannot be measured using conventional bulk and local measurement techniques. Here, we report direct and spatially resolved experimental measurements of the nonlinear stresses surrounding colloidal crystalline defect cores, and show that the stresses at vacancy cores generate attractive interactions between them. We also directly visualize the softening of crystalline regions surrounding dislocation cores, and find that stress fluctuations in quiescent polycrystals are uniformly distributed rather than localized at grain boundaries, as is the case in strained atomic polycrystals. Nonlinear stress measurements have important implications for strain hardening, yield, and fatigue.

cond-mat.mtrl-sci↗

arXiv2016

Pinning Susceptibility: The effect of dilute, quenched disorder on jamming

We study the effect of dilute pinning on the jamming transition. Pinning reduces the average contact number needed to jam unpinned particles and shifts the jamming threshold to lower densities, leading to a pinning susceptibility, $χ_p$. Our main results are that this susceptibility obeys scaling form and diverges in the thermodynamic limit as $χ_p \propto |ϕ- ϕ_c^\infty|^{-γ_p}$ where $ϕ_c^\infty$ is the jamming threshold in the absence of pins. Finite-size scaling arguments yield these values with associated statistical (systematic) errors $γ_p = 1.018 \pm 0.026 (0.291) $ in $d=2$ and $γ_p =1.534 \pm 0.120 (0.822)$ in $d=3$. Logarithmic corrections raise the exponent in $d=2$ to close to the $d=3$ value, although the systematic errors are very large.

cond-mat.soft↗