David C. Roberts

Mapping the Evolution of Scientific Fields

Despite the apparent cross-disciplinary interactions among scientific fields, a formal description of their evolution is lacking. Here we describe a novel approach to study the dynamics and evolution of scientific fields using a network-based analysis. We build an idea network consisting of American Physical Society Physics and Astronomy Classification Scheme (PACS) numbers as nodes representing scientific concepts. Two PACS numbers are linked if there exist publications that reference them simultaneously. We locate scientific fields using a community finding algorithm, and describe the time evolution of these fields over the course of 1985–2006. The communities we identify map to known scientific fields, and their age depends on their size and activity. We expect our approach to quantifying the evolution of ideas to be relevant for making predictions about the future of science and thus help to guide its development.

Using Expression and Genotype to Predict Drug Response in Yeast

Personalized, or genomic, medicine entails tailoring pharmacological therapies according to individual genetic variation at genomic loci encoding proteins in drug-response pathways. It has been previously shown that steady-state mRNA expression can be used to predict the drug response (i.e., sensitivity or resistance) of non-genotyped mammalian cancer cell lines to chemotherapeutic agents. In a real-world setting, clinicians would have access to both steady-state expression levels of patient tissue(s) and a patients genotypic profile, and yet the predictive power of transcripts versus markers is not well understood. We have previously shown that a collection of genotyped and expression-profiled yeast strains can provide a model for personalized medicine. Here we compare the predictive power of 6,229 steady-state mRNA transcript levels and 2,894 genotyped markers using a pattern recognition algorithm. We were able to predict with over 70% accuracy the drug sensitivity of 104 individual genotyped yeast strains derived from a cross between a laboratory strain and a wild isolate. We observe that, independently of drug mechanism of action, both transcripts and markers can accurately predict drug response. Marker-based prediction is usually more accurate than transcript-based prediction, likely reflecting the genetic determination of gene expression in this cross.

Finite-time collapse of N classical fields described by coupled nonlinear Schrödinger equations

We prove the finite-time collapse of a system of N classical fields, which are described by N coupled nonlinear Schrödinger equations. We derive the conditions under which all of the fields experiences this finite-time collapse. Finally, for two-dimensional systems, we derive constraints on the number of particles associated with each field that are necessary to prevent collapse.

Linear reformulation of the Kuramoto model of self-synchronizing coupled oscillators

The present paper introduces a linear reformulation of the Kuramoto model describing a self-synchronizing phase transition in a system of globally coupled oscillators that in general have different characteristic frequencies. The reformulated model provides an alternative coherent framework through which one can analytically tackle synchronization problems that are not amenable to the original Kuramoto analysis. It allows one to solve explicitly for the synchronization order parameter and the critical point of (1) the full phase-locking transition for a system with a finite number of oscillators (unlike the original Kuramoto model, which is solvable implicitly only in the mean-field limit) and (2) a new class of continuum systems. It also makes it possible to probe the systems dynamics as it moves toward a steady state. While discussion in this paper is restricted to systems with global coupling, the formalism introduced by the linear reformulation also lends itself to solving systems that exhibit local or asymmetric coupling.

Drag force on an impurity below the superfluid critical velocity in a quasi-one-dimensional Bose-Einstein condensate

The existence of frictionless flow below a critical velocity for obstacles moving in a superfluid is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a nonzero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the Doppler shifts of reflected quantum fluctuations from either side of the impurity. Our calculation is based on a consistent extension of Bogoliubov theory to second order in the interaction strength, and finds new analytical solutions to the Bogoliubov-de Gennes equations for a gray soliton. Our results raise questions regarding the quantum dynamics in the formation of persistent currents in superfluids.

Hydrodynamic boundary condition for superfluid flow

We discuss the hydrodynamic boundary condition for a superfluid moving tangentially to a rough surface. Specifically, we argue that the scattering of quantum fluctuations off surface roughness affects the nature of the boundary condition, and that this has important consequences including a theorized critical speed and the presence of normal fluid at any nonzero speed, even if the boundary is held at zero temperature (i.e., a moving superfluid flow creates a sustained temperature difference between the superfluid and the boundary). This hydrodynamic boundary condition is relevant not only for superfluid helium experiments but also for experiments with trapped dilute Bose-Einstein condensates, in particular, those involving atomic waveguides near surfaces.

Impurity crystal in a bose-einstein condensate.

We investigate the behavior of impurity fields immersed in a larger condensate field in various dimensions. We discuss the localization of a single impurity field within a condensate and note the effects of surface energy. We derive the functional form of the attractive condensate-mediated interaction between two impurities. Generalizing the analysis to N impurity fields, we show that within various parameter regimes a crystal of impurity fields can form spontaneously in the condensate. Finally, the system of condensate and crystallized impurity structure is shown to have nonclassical rotational inertia, which is characteristic of superfluidity; i.e., the system can be seen to exhibit supersolid behavior.

When superfluids are a drag

The article considers the dramatic phenomenon of seemingly frictionless flow of slow-moving superfluids. Specifically the question of whether an object in a superfluid flow experiences any drag force is addressed. A brief account is given of the history of this problem and it is argued that recent advances in ultracold atomic physics can shed much new light on this problem. The article presents the commonly held notion that sufficiently slow-moving superfluids can flow without drag and also discusses research suggesting that scattering quantum fluctuations might cause drag in a superfluid moving at any speed.