arXiv subjects

James P. Sethna

Publications and source records attributed to James P. Sethna.

At least 109 records · Page 6Linked to original sources

arXiv2009

Discontinuities at the DNA supercoiling transition

While slowly turning the ends of a single molecule of DNA at constant applied force, a discontinuity was recently observed at the supercoiling transition, when a small plectoneme is suddenly formed. This can be understood as an abrupt transition into a state in which stretched and plectonemic DNA coexist. We argue that there should be discontinuities in both the extension and the torque at the transition, and provide experimental evidence for both. To predict the sizes of these discontinuities and how they change with the overall length of DNA, we organize a theory for the coexisting plectonemic state in terms of four length-independent parameters. We also test plectoneme theories, including our own elastic rod simulation, finding discrepancies with experiment that can be understood in terms of the four coexisting state parameters.

q-bio.BM↗

arXiv2009

Order Parameters, Broken Symmetry, and Topology

We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several examples. We discuss elementary excitations and the topological theory of defects.

cond-mat↗

arXiv2008

Temperature dependence of the superheating field for superconductors in the high-k London limit

We study the metastability of the superheated Meissner state in type II superconductors with k >> 1 beyond Ginzburg-Landau theory, which is applicable only in the vicinity of the critical temperature. Within Eilenberger's semiclassical approximation, we use the local electrodynamic response of the superconductor to derive a generalized thermodynamic potential valid at any temperature. The stability analysis of this functional yields the temperature dependence of the superheating field. Finally, we comment on the implications of our results for superconducting cavities in particle accelerators.

cond-mat.supr-con↗

arXiv2008

Variational method for estimating the rate of convergence of Markov Chain Monte Carlo algorithms

We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on approximating the second largest eigenvalue in the spectrum of the MCMC operator using a variational principle and the approach is applicable to problems with continuous state spaces. We apply the method to one dimensional examples with Gaussian and quartic target densities, and we contrast the performance of the Random Walk Metropolis-Hastings (RWMH) algorithm with a ``smart'' variant that incorporates gradient information into the trial moves. We find that the variational method agrees quite closely with numerical simulations. We also see that the smart MCMC algorithm often fails to converge geometrically in the tails of the target density except in the simplest case we examine, and even then care must be taken to choose the appropriate scaling of the deterministic and random parts of the proposed moves. Again, this calls into question the utility of smart MCMC in more complex problems. Finally, we apply the same method to approximate the rate of convergence in multidimensional Gaussian problems with and without importance sampling. There we demonstrate the necessity of importance sampling for target densities which depend on variables with a wide range of scales.

physics.data-an↗

arXiv2008

Anomalous Conductance Oscillations and Half-Metallicity in Atomic Ag-O Chains

Using spin density functional theory we study the electronic and magnetic properties of atomically thin, suspended chains containing silver and oxygen atoms in an alternating sequence. Chains longer than 4 atoms develop a half-metallic ground state implying fully spin polarized charge carriers. The conductances of the chains exhibit weak even-odd oscillations around an anomalously low value of 0.1G_0 (G_0 = 2e^2h) which coincide with the averaged experimental conductance in the long chain limit. The unusual conductance properties are explained in terms of a resonating-chain model which takes the reflection probability and phase-shift of a single bulk-chain interface as the only input. The model also explains the conductance oscillations for other metallic chains.

cond-mat.mes-hall↗

arXiv2008

Sloppiness, robustness, and evolvability in systems biology

The functioning of many biochemical networks is often robust -- remarkably stable under changes in external conditions and internal reaction parameters. Much recent work on robustness and evolvability has focused on the structure of neutral spaces, in which system behavior remains invariant to mutations. Recently we have shown that the collective behavior of multiparameter models is most often 'sloppy': insensitive to changes except along a few 'stiff' combinations of parameters, with an enormous sloppy neutral subspace. Robustness is often assumed to be an emergent evolved property, but the sloppiness natural to biochemical networks offers an alternative non-adaptive explanation. Conversely, ideas developed to study evolvability in robust systems can be usefully extended to characterize sloppy systems.

q-bio.QM↗

arXiv2008

Challenges in continuum modeling of intergranular fracture

Intergranular fracture in polycrystals is often simulated by finite elements coupled to a cohesive-zone model for the interfaces, requiring cohesive laws for grain boundaries as a function of their geometry. We discuss three challenges in understanding intergranular fracture in polycrystals. First, 3D grain boundary geometries comprise a five dimensional space. Second, the energy and peak stress of grain boundaries have singularities for all commensurate grain boundaries, especially those with short repeat distances. Thirdly, fracture nucleation and growth depends not only upon the properties of grain boundaries, but in crucial ways on edges, corners, and triple junctions of even greater geometrical complexity. To address the first two challenges, we explore the physical underpinnings for creating functional forms to capture the heirarchical commensurability structure in the grain boundary properties. To address the last challenge, we demonstrate a method for atomistically extracting the fracture properties of geometrically complex local regions on the fly from within a finite element simulation.

cond-mat.other↗

arXiv2008

A comparison of finite element and atomistic modelling of fracture

Are the cohesive laws of interfaces sufficient for modelling fracture in polycrystals using the cohesive zone model? We examine this question by comparing a fully atomistic simulation of a silicon polycrystal to a finite element simulation with a similar overall geometry. The cohesive laws used in the finite element simulation are measured atomistically. We describe in detail how to convert the output of atomistic grain boundary fracture simulations into the piecewise linear form needed by a cohesive zone model. We discuss the effects of grain boundary microparameters (the choice of section of the interface, the translations of the grains relative to one another, and the cutting plane of each lattice orientation) on the cohesive laws and polycrystal fracture. We find that the atomistic simulations fracture at lower levels of external stress, indicating that the initiation of fracture in the atomistic simulations is likely dominated by irregular atomic structures at external faces, internal edges, corners, and junctions of grains. Thus, cohesive properties of interfaces alone are likely not sufficient for modelling the fracture of polycrystals using continuum methods.

cond-mat.mtrl-sci↗

arXiv2008

Grain boundary energies and cohesive strength as a function of geometry

Cohesive laws are stress-strain curves used in finite element calculations to describe the debonding of interfaces such as grain boundaries. It would be convenient to describe grain boundary cohesive laws as a function of the parameters needed to describe the grain boundary geometry; two parameters in 2D and 5 parameters in 3D. However, we find that the cohesive law is not a smooth function of these parameters. In fact, it is discontinuous at geometries for which the two grains have repeat distances that are rational with respect to one another. Using atomistic simulations, we extract grain boundary energies and cohesive laws of grain boundary fracture in 2D with a Lennard-Jones potential for all possible geometries which can be simulated within periodic boundary conditions with a maximum box size. We introduce a model where grain boundaries are represented as high symmetry boundaries decorated by extra dislocations. Using it, we develop a functional form for the symmetric grain boundary energies, which have cusps at all high symmetry angles. We also find the asymptotic form of the fracture toughness near the discontinuities at high symmetry grain boundaries using our dislocation decoration model.

cond-mat.mtrl-sci↗

arXiv2007

Phonon Overlaps: Polyacetylene, Polarons, and Molecular Size

We provide a theory for the effects of polarons and phonons in mediating and suppressing the quantum tunneling of electrons into single molecules of conducting polymers, motivated by experiments on molecular quantum dots. The effects of both phonons and excitations of the polaron particle-in-a-box excitations are calculated. Using both the Su-Schrieffer-Heeger (SSH) model of polyacetylene and direct density-functional theory (DFT) calculations, we calculate the suppression of ground--state to ground--state transitions and the position and strength of the side-bands.

cond-mat.mes-hall↗

arXiv2007

Universally Sloppy Parameter Sensitivities in Systems Biology

Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring \emph{in vivo} biochemical parameters is difficult, and collectively fitting them to other data often yields large parameter uncertainties. Nevertheless, in earlier work we showed in a growth-factor-signaling model that collective fitting could yield well-constrained predictions, even when it left individual parameters very poorly constrained. We also showed that the model had a `sloppy' spectrum of parameter sensitivities, with eigenvalues roughly evenly distributed over many decades. Here we use a collection of models from the literature to test whether such sloppy spectra are common in systems biology. Strikingly, we find that every model we examine has a sloppy spectrum of sensitivities. We also test several consequences of this sloppiness for building predictive models. In particular, sloppiness suggests that collective fits to even large amounts of ideal time-series data will often leave many parameters poorly constrained. Tests over our model collection are consistent with this suggestion. This difficulty with collective fits may seem to argue for direct parameter measurements, but sloppiness also implies that such measurements must be formidably precise and complete to usefully constrain many model predictions. We confirm this implication in our signaling model. Our results suggest that sloppy sensitivity spectra are universal in systems biology models. The prevalence of sloppiness highlights the power of collective fits and suggests that modelers should focus on predictions rather than on parameters.

q-bio.QM↗

arXiv2007

Extracting falsifiable predictions from sloppy models

Successful predictions are among the most compelling validations of any model. Extracting falsifiable predictions from nonlinear multiparameter models is complicated by the fact that such models are commonly sloppy, possessing sensitivities to different parameter combinations that range over many decades. Here we discuss how sloppiness affects the sorts of data that best constrain model predictions, makes linear uncertainty approximations dangerous, and introduces computational difficulties in Monte-Carlo uncertainty analysis. We also present a useful test problem and suggest refinements to the standards by which models are communicated.

q-bio.QM↗

arXiv2007

Stress-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density tensor

We derive general relations between grain boundaries, rotational deformations, and stress-free states for the mesoscale continuum Nye dislocation density tensor. Dislocations generally are associated with long-range stress fields. We provide the general form for dislocation density fields whose stress fields vanish. We explain that a grain boundary (a dislocation wall satisfying Frank's formula) has vanishing stress in the continuum limit. We show that the general stress-free state can be written explicitly as a (perhaps continuous) superposition of flat Frank walls. We show that the stress-free states are also naturally interpreted as configurations generated by a general spatially-dependent rotational deformation. Finally, we propose a least-squares definition for the spatially-dependent rotation field of a general (stressful) dislocation density field.

cond-mat.dis-nn↗

arXiv2006

Crackling Noise and Avalanches: Scaling, Critical Phenomena, and the Renormalization Group

In the past two decades or so, we have learned how to understand crackling noise in a wide variety of systems. We review here the basic ideas and methods we use to understand crackling noise - critical phenomena, universality, the renormalization group, power laws, and universal scaling functions. These methods and tools were originally developed to understand continuous phase transitions in thermal and disordered systems, and we also introduce these more traditional applications as illustrations of the basic ideas and phenomena.

cond-mat.dis-nn↗

arXiv2006

Phonons in Molecular Quantum Dots: Density Functional Calculation of Franck-Condon Emission Rates in External Fields

We report the calculation of various phonon overlaps and their corresponding phonon emission probabilities for the problem of an electron tunneling onto and off of the buckyball-dimer molecular quantum dot $C_{72}$, both with and without the influence of an external field. We show that the stretch mode of the two balls of the dumbbell couples most strongly to the electronic transition, and in turn that a field in the direction of the bond between the two $C_{36}$ balls is most effective at further increasing the phonon emission into the stretch mode. As the field is increased, phonon emission increases in probability with an accompanying decrease in probability of the dot remaining in the ground vibrational state. We also present a simple model to gauge the effect of molecular size on the phonon emission of molecules similar to our $C_{72}$ molecule, including the experimentally tested $C_{140}$. In our approach we do not assume that the hessians of the molecule are identical for different charge states. Our treatment is hence a generalization of the traditional phonon overlap calculations for coupled electron-photon transition in solids.

cond-mat.mes-hall↗

arXiv2006

Optimal experimental design in an EGFR signaling and down-regulation model

We apply the methods of optimal experimental design to a differential equation model for epidermal growth factor receptor (EGFR) signaling, trafficking, and down-regulation. The model incorporates the role of a recently discovered protein complex made up of the E3 ubiquitin ligase, Cbl, the guanine exchange factor (GEF), Cool-1 (Beta-Pix), and the Rho family G protein Cdc42. The complex has been suggested to be important in disrupting receptor down-regulation. We demonstrate that the model interactions can accurately reproduce the experimental observations, that they can be used to make predictions with accompanying uncertainties, and that we can apply ideas of optimal experimental design to suggest new experiments that reduce the uncertainty on unmeasurable components of the system.

q-bio.MN↗

arXiv2006

The sloppy model universality class and the Vandermonde matrix

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy; the system behavior depends only on a few `stiff' combinations of the parameters and is unchanged as other `sloppy' parameter combinations vary by orders of magnitude. We contrast examples of sloppy models (from systems biology, variational quantum Monte Carlo, and common data fitting) with systems which are not sloppy (multidimensional linear regression, random matrix ensembles). We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form, with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.

cond-mat.stat-mech↗

arXiv2006

Mesoscale theory of grains and cells: crystal plasticity and coarsening

Solids with spatial variations in the crystalline axes naturally evolve into cells or grains separated by sharp walls. Such variations are mathematically described using the Nye dislocation density tensor. At high temperatures, polycrystalline grains form from the melt and coarsen with time: the dislocations can both climb and glide. At low temperatures under shear the dislocations (which allow only glide) form into cell structures. While both the microscopic laws of dislocation motion and the macroscopic laws of coarsening and plastic deformation are well studied, we hitherto have had no simple, continuum explanation for the evolution of dislocations into sharp walls. We present here a mesoscale theory of dislocation motion. It provides a quantitative description of deformation and rotation, grounded in a microscopic order parameter field exhibiting the topologically conserved quantities. The topological current of the Nye dislocation density tensor is derived from a microscopic theory of glide driven by Peach-Koehler forces between dislocations using a simple closure approximation. The resulting theory is shown to form sharp dislocation walls in finite time, both with and without dislocation climb.

cond-mat.mtrl-sci↗