# Browsing by Subject "Physical Sciences"

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Item Open Access (0,2) hybrid models(Journal of High Energy Physics, 2018-09-01) Bertolini, M; Plesser, MR© 2018, The Author(s). We introduce a class of (0,2) superconformal field theories based on hybrid geometries, generalizing various known constructions. We develop techniques for the computation of the complete massless spectrum when the theory can be interpreted as determining a perturbative heterotic string compactification. We provide evidence for surprising properties regarding RG flows and IR accidental symmetries in (0,2) hybrid CFTs. We also study the conditions for embedding a hybrid theory in a particular class of gauged linear sigma models. This perspective suggests that our construction generates models which cannot be realized or analyzed by previously known methods.Item Open Access (1,1) L-space knots(COMPOSITIO MATHEMATICA, 2018-05-01) Greene, JE; Lewallen, S; Vafaee, FWe characterize the (1, 1) knots in the three-sphere and lens spaces that admit non-trivial L-space surgeries. As a corollary, 1-bridge braids in these manifolds admit non- trivial L-space surgeries. We also recover a characterization of the Berge manifold amongst 1-bridge braid exteriors.Item Open Access A baseline paleoecological study for the Santa Cruz Formation (late–early Miocene) at the Atlantic coast of Patagonia, Argentina(Palaeogeography, Palaeoclimatology, Palaeoecology, 2010-06) Vizcaíno, SF; Bargo, MS; Kay, RF; Fariña, RA; Di Giacomo, M; Perry, JMG; Prevosti, FJ; Toledo, N; Cassini, GH; Fernicola, JCCoastal exposures of the Santa Cruz Formation (late-early Miocene, southern Patagonia, Argentina) between the Coyle and Gallegos rivers have been a fertile ground for recovery of Miocene vertebrates for more than 100 years. The formation contains an exceptionally rich mammal fauna, which documents a vertebrate assemblage very different from any living community, even at the ordinal level. Intensive fieldwork performed since 2003 (nearly 1200 specimens have been collected, including marsupials, xenarthrans, notoungulates, litopterns astrapotheres, rodents, and primates) document this assertion. The goal of this study is to attempt to reconstruct the trophic structure of the Santacrucian mammalian community with precise stratigraphic control. Particularly, we evaluate the depauperate carnivoran paleoguild and identify new working hypotheses about this community. A database has been built from about 390 specimens from two localities: Campo Barranca (CB) and Puesto Estancia La Costa (PLC). All species have been classified as herbivore or carnivore, their body masses estimated, and the following parameters estimated: population density, on-crop biomass, metabolic rates, and the primary and secondary productivity. According to our results, this model predicts an imbalance in both CB and PLC faunas which can be seen by comparing the secondary productivity of the ecosystem and the energetic requirements of the carnivores in it. While in CB, the difference between carnivores and herbivores is six-fold, in PLC this difference is smaller, the secondary productivity is still around three times that of the carnivore to herbivore ratio seen today. If both localities are combined, the difference rises to around four-fold in favour of secondary productivity. Finally, several working hypotheses about the Santacrucian mammalian community and the main lineages of herbivores and carnivores are offered. © 2010 Elsevier B.V. All rights reserved.Item Open Access A classical proof that the algebraic homotopy class of a rational function is the residue pairing(Linear Algebra and Its Applications, 2020-06-15) Kass, JL; Wickelgren, K© 2020 Elsevier Inc. Cazanave has identified the algebraic homotopy class of a rational function of 1 variable with an explicit nondegenerate symmetric bilinear form. Here we show that Hurwitz's proof of a classical result about real rational functions essentially gives an alternative proof of the stable part of Cazanave's result. We also explain how this result can be interpreted in terms of the residue pairing and that this interpretation relates the result to the signature theorem of Eisenbud, Khimshiashvili, and Levine, showing that Cazanave's result answers a question posed by Eisenbud for polynomial functions in 1 variable. Finally, we announce results answering this question for functions in an arbitrary number of variables.Item Open Access A formal Anthropocene is compatible with but distinct from its diachronous anthropogenic counterparts: a response to W.F. Ruddiman’s ‘three flaws in defining a formal Anthropocene’(Progress in Physical Geography, 2019-06-01) Zalasiewicz, J; Waters, CN; Head, MJ; Poirier, C; Summerhayes, CP; Leinfelder, R; Grinevald, J; Steffen, W; Syvitski, J; Haff, P; McNeill, JR; Wagreich, M; Fairchild, IJ; Richter, DD; Vidas, D; Williams, M; Barnosky, AD; Cearreta, A© The Author(s) 2019. We analyse the ‘three flaws’ to potentially defining a formal Anthropocene geological time unit as advanced by Ruddiman (2018). (1) We recognize a long record of pre-industrial human impacts, but note that these increased in relative magnitude slowly and were strongly time-transgressive by comparison with the extraordinarily rapid, novel and near-globally synchronous changes of post-industrial time. (2) The rules of stratigraphic nomenclature do not ‘reject’ pre-industrial anthropogenic signals – these have long been a key characteristic and distinguishing feature of the Holocene. (3) In contrast to the contention that classical chronostratigraphy is now widely ignored by scientists, it remains vital and widely used in unambiguously defining geological time units and is an indispensable part of the Earth sciences. A mounting body of evidence indicates that the Anthropocene, considered as a precisely defined geological time unit that begins in the mid-20th century, is sharply distinct from the Holocene.Item Open Access A hybrid ion-atom trap with integrated high resolution mass spectrometer(Review of Scientific Instruments, 2019-10-01) Jyothi, S; Egodapitiya, KN; Bondurant, B; Jia, Z; Pretzsch, E; Chiappina, P; Shu, G; Brown, KR© 2019 Author(s). In this article, we describe the design, construction, and implementation of our ion-atom hybrid system incorporating a high resolution time of flight mass spectrometer (TOFMS). Potassium atoms (39K) in a magneto optical trap and laser cooled calcium ions (40Ca+) in a linear Paul trap are spatially overlapped, and the combined trap is integrated with a TOFMS for radial extraction and detection of reaction products. We also present some experimental results showing interactions between 39K+ and 39K, 40Ca+ and 39K+, as well as 40Ca+ and 39K pairs. Finally, we discuss prospects for cooling CaH+ molecular ions in the hybrid ion-atom system.Item Open Access A microscopic model of the Stokes-Einstein relation in arbitrary dimension.(The Journal of chemical physics, 2018-06) Charbonneau, Benoit; Charbonneau, Patrick; Szamel, GrzegorzThe Stokes-Einstein relation (SER) is one of the most robust and widely employed results from the theory of liquids. Yet sizable deviations can be observed for self-solvation, which cannot be explained by the standard hydrodynamic derivation. Here, we revisit the work of Masters and Madden [J. Chem. Phys. 74, 2450-2459 (1981)], who first solved a statistical mechanics model of the SER using the projection operator formalism. By generalizing their analysis to all spatial dimensions and to partially structured solvents, we identify a potential microscopic origin of some of these deviations. We also reproduce the SER-like result from the exact dynamics of infinite-dimensional fluids.Item Open Access A slicing obstruction from the $\frac {10}{8}$ theorem(Proceedings of the American Mathematical Society, 2016-08-29) Donald, A; Vafaee, F© 2016 American Mathematical Society. From Furuta’s 10/8 theorem, we derive a smooth slicing obstruction for knots in S3 using a spin 4-manifold whose boundary is 0-surgery on a knot. We show that this obstruction is able to detect torsion elements in the smooth concordance group and find topologically slice knots which are not smoothly slice.Item Open Access A stochastic-Lagrangian particle system for the Navier-Stokes equations(Nonlinearity, 2008-11-01) Iyer, Gautam; Mattingly, JonathanThis paper is based on a formulation of the Navier-Stokes equations developed by Constantin and the first author (Commun. Pure Appl. Math. at press, arXiv:math.PR/0511067), where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. In this paper, we take N copies of the above process (each based on independent Wiener processes), and replace the expected value with 1/N times the sum over these N copies. (We note that our formulation requires one to keep track of N stochastic flows of diffeomorphisms, and not just the motion of N particles.) We prove that in two dimensions, this system of interacting diffeomorphisms has (time) global solutions with initial data in the space C1,α which consists of differentiable functions whose first derivative is α Hölder continuous (see section 3 for the precise definition). Further, we show that as N → ∞ the system converges to the solution of Navier-Stokes equations on any finite interval [0, T]. However for fixed N, we prove that this system retains roughly O(1/N) times its original energy as t → ∞. Hence the limit N → ∞ and T → ∞ do not commute. For general flows, we only provide a lower bound to this effect. In the special case of shear flows, we compute the behaviour as t → ∞ explicitly. © 2008 IOP Publishing Ltd and London Mathematical Society.Item Open Access An adaptive Euler-Maruyama scheme for SDEs: Convergence and stability(IMA Journal of Numerical Analysis, 2007-01-01) Lamba, H; Mattingly, JC; Stuart, AMThe understanding of adaptive algorithms for stochastic differential equations (SDEs) is an open area, where many issues related to both convergence and stability (long-time behaviour) of algorithms are unresolved. This paper considers a very simple adaptive algorithm, based on controlling only the drift component of a time step. Both convergence and stability are studied. The primary issue in the convergence analysis is that the adaptive method does not necessarily drive the time steps to zero with the user-input tolerance. This possibility must be quantified and shown to have low probability. The primary issue in the stability analysis is ergodicity. It is assumed that the noise is nondegenerate, so that the diffusion process is elliptic, and the drift is assumed to satisfy a coercivity condition. The SDE is then geometrically ergodic (averages converge to statistical equilibrium exponentially quickly). If the drift is not linearly bounded, then explicit fixed time step approximations, such as the Euler-Maruyama scheme, may fail to be ergodic. In this work, it is shown that the simple adaptive time-stepping strategy cures this problem. In addition to proving ergodicity, an exponential moment bound is also proved, generalizing a result known to hold for the SDE itself. © The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.Item Open Access An Empirical Comparison of Multiple Imputation Methods for Categorical Data(The American Statistician, 2017-04-03) Akande, O; Li, F; Reiter, J© 2017 American Statistical Association. Multiple imputation is a common approach for dealing with missing values in statistical databases. The imputer fills in missing values with draws from predictive models estimated from the observed data, resulting in multiple, completed versions of the database. Researchers have developed a variety of default routines to implement multiple imputation; however, there has been limited research comparing the performance of these methods, particularly for categorical data. We use simulation studies to compare repeated sampling properties of three default multiple imputation methods for categorical data, including chained equations using generalized linear models, chained equations using classification and regression trees, and a fully Bayesian joint distribution based on Dirichlet process mixture models. We base the simulations on categorical data from the American Community Survey. In the circumstances of this study, the results suggest that default chained equations approaches based on generalized linear models are dominated by the default regression tree and Bayesian mixture model approaches. They also suggest competing advantages for the regression tree and Bayesian mixture model approaches, making both reasonable default engines for multiple imputation of categorical data. Supplementary material for this article is available online.Item Open Access An energetic variational approach for ION transport(Communications in Mathematical Sciences, 2014-03-06) Xu, S; Sheng, P; Liu, CThe transport and distribution of charged particles are crucial in the study of many physical and biological problems. In this paper, we employ an Energy Variational Approach to derive the coupled Poisson-Nernst-Planck-Navier-Stokes system. All of the physics is included in the choices of corresponding energy law and kinematic transport of particles. The variational derivations give the coupled force balance equations in a unique and deterministic fashion. We also discuss the situations with different types of boundary conditions. Finally, we show that the Onsager's relation holds for the electrokinetics, near the initial time of a step function applied field. © 2014 International Press.Item Open Access An energy stable C^{0}finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density(Journal of Computational Physics, 2020-03-15) Shen, L; Huang, H; Lin, P; Song, Z; Xu, SIn this paper, we focus on modeling and simulation of two-phase flow problems with moving contact lines and variable density. A thermodynamically consistent phase-field model with general Navier boundary condition is developed based on the concept of quasi-incompressibility and the energy variational method. A mass conserving C0 finite element scheme is proposed to solve the PDE system. Energy stability is achieved at the fully discrete level. Various numerical results confirm that the proposed scheme for both P1 element and P2 element are energy stable.Item Open Access An improved approach to age-modeling in deep time: Implications for the Santa Cruz Formation, Argentina(Bulletin of the Geological Society of America, 2020-01-01) Trayler, RB; Schmitz, MD; Cuitiño, JI; Kohn, MJ; Bargo, MS; Kay, RF; Strömberg, CAE; Vizcaíno, SF© 2019 Geological Society of America. Accurate age-depth models for proxy records are crucial for inferring changes to the environment through space and time, yet traditional methods of constructing these models assume unrealistically small age uncertainties and do not account for many geologic complexities. Here we modify an existing Bayesian age-depth model to foster its application for deep time U-Pb and 40Ar/39Ar geochronology. More flexible input likelihood functions and use of an adaptive proposal algorithm in the Markov Chain Monte Carlo engine better account for the age variability often observed in magmatic crystal populations, whose dispersion can reflect inheritance, crystal residence times and daughter isotope loss. We illustrate this approach by calculating an age-depth model with a contiguous and realistic uncertainty envelope for the Miocene Santa Cruz Formation (early Miocene; Burdigalian), Argentina. The model is calibrated using new, high-precision isotope dilution U-Pb zircon ages for stratigraphically located interbedded tuffs, whose weighted mean ages range from ca. 16.78 ± 0.03 Ma to 17.62 ± 0.03 Ma. We document how the Bayesian age-depth model objectively reallocates probability across the posterior ages of dated horizons, and thus produces better estimates of relative ages among strata and variations in sedimentation rate. We also present a simple method to propagate age-depth model uncertainties onto stratigraphic proxy data using a Monte Carlo technique. This approach allows us to estimate robust uncertainties on isotope composition through time, important for comparisons of terrestrial systems to other proxy records.Item Open Access Analyzing X-ray tomographies of granular packings.(The Review of scientific instruments, 2017-05) Weis, Simon; Schröter, MatthiasStarting from three-dimensional volume data of a granular packing, as, e.g., obtained by X-ray Computed Tomography, we discuss methods to first detect the individual particles in the sample and then analyze their properties. This analysis includes the pair correlation function, the volume and shape of the Voronoi cells, and the number and type of contacts formed between individual particles. We mainly focus on packings of monodisperse spheres, but we will also comment on other monoschematic particles such as ellipsoids and tetrahedra. This paper is accompanied by a package of free software containing all programs (including source code) and an example three-dimensional dataset which allows the reader to reproduce and modify all examples given.Item Open Access Anomalous dissipation in a stochastically forced infinite-dimensional system of coupled oscillators(Journal of Statistical Physics, 2007-09-01) Mattingly, JC; Suidan, TM; Vanden-Eijnden, EWe study a system of stochastically forced infinite-dimensional coupled harmonic oscillators. Although this system formally conserves energy and is not explicitly dissipative, we show that it has a nontrivial invariant probability measure. This phenomenon, which has no finite dimensional equivalent, is due to the appearance of some anomalous dissipation mechanism which transports energy to infinity. This prevents the energy from building up locally and allows the system to converge to the invariant measure. The invariant measure is constructed explicitly and some of its properties are analyzed. © 2007 Springer Science+Business Media, LLC.Item Open Access Ballistic Graphene Josephson Junctions from the Short to the Long Junction Regimes.(Physical review letters, 2016-12-02) Borzenets, IV; Amet, F; Ke, CT; Draelos, AW; Wei, MT; Seredinski, A; Watanabe, K; Taniguchi, T; Bomze, Y; Yamamoto, M; Tarucha, S; Finkelstein, GWe investigate the critical current I_{C} of ballistic Josephson junctions made of encapsulated graphene-boron-nitride heterostructures. We observe a crossover from the short to the long junction regimes as the length of the device increases. In long ballistic junctions, I_{C} is found to scale as ∝exp(-k_{B}T/δE). The extracted energies δE are independent of the carrier density and proportional to the level spacing of the ballistic cavity. As T→0 the critical current of a long (or short) junction saturates at a level determined by the product of δE (or Δ) and the number of the junction's transversal modes.Item Open Access Behavior of different numerical schemes for random genetic drift(BIT Numerical Mathematics, 2019-09-01) Xu, S; Chen, M; Liu, C; Zhang, R; Yue, XIn the problem of random genetic drift, the probability density of one gene is governed by a degenerated convection-dominated diffusion equation. Dirac singularities will always be developed at boundary points as time evolves, which is known as the fixation phenomenon in genetic evolution. Three finite volume methods: FVM1-3, one central difference method: FDM1 and three finite element methods: FEM1-3 are considered. These methods lead to different equilibrium states after a long time. It is shown that only schemes FVM3 and FEM3, which are the same, preserve probability, expectation and positiveness and predict the correct probability of fixation. FVM1-2 wrongly predict the probability of fixation due to their intrinsic viscosity, even though they are unconditionally stable. Contrarily, FDM1 and FEM1-2 introduce different anti-diffusion terms, which make them unstable and fail to preserve positiveness.Item Open Access Berge–Gabai knots and L–space satellite operations(Algebraic & Geometric Topology, 2015-01-15) Hom, J; Lidman, T; Vafaee, F© 2014 Mathematical Sciences Publishers. All rights reserved. Let P(K) be a satellite knot where the pattern P is a Berge–Gabai knot (ie a knot in the solid torus with a nontrivial solid torus Dehn surgery) and the companion K is a nontrivial knot in S3. We prove that P(K) is an L–space knot if and only if K is an L–space knot and P is sufficiently positively twisted relative to the genus of K. This generalizes the result for cables due to Hedden [13] and Hom [17].Item Open Access BigSMILES: A Structurally-Based Line Notation for Describing Macromolecules.(ACS central science, 2019-09-12) Lin, Tzyy-Shyang; Coley, Connor W; Mochigase, Hidenobu; Beech, Haley K; Wang, Wencong; Wang, Zi; Woods, Eliot; Craig, Stephen L; Johnson, Jeremiah A; Kalow, Julia A; Jensen, Klavs F; Olsen, Bradley DHaving a compact yet robust structurally based identifier or representation system is a key enabling factor for efficient sharing and dissemination of research results within the chemistry community, and such systems lay down the essential foundations for future informatics and data-driven research. While substantial advances have been made for small molecules, the polymer community has struggled in coming up with an efficient representation system. This is because, unlike other disciplines in chemistry, the basic premise that each distinct chemical species corresponds to a well-defined chemical structure does not hold for polymers. Polymers are intrinsically stochastic molecules that are often ensembles with a distribution of chemical structures. This difficulty limits the applicability of all deterministic representations developed for small molecules. In this work, a new representation system that is capable of handling the stochastic nature of polymers is proposed. The new system is based on the popular "simplified molecular-input line-entry system" (SMILES), and it aims to provide representations that can be used as indexing identifiers for entries in polymer databases. As a pilot test, the entries of the standard data set of the glass transition temperature of linear polymers (Bicerano, 2002) were converted into the new BigSMILES language. Furthermore, it is hoped that the proposed system will provide a more effective language for communication within the polymer community and increase cohesion between the researchers within the community.