Abstract:
Graphene nanoribbon interconnects are fabricated, and the extracted resistivity is compared to that of Cu. It is found that the average resistivity at a given line-width (18nm

Abstract:
Graphene nanoribbons (GNRs) with widths down to 16 nm have been characterized for their current-carrying capacity. It is found that GNRs exhibit an impressive breakdown current density, on the order of 10^8 A/cm2. The breakdown current density is found to have a reciprocal relationship to GNR resistivity and the data fit points to Joule heating as the likely mechanism of breakdown. The superior current-carrying capacity of GNRs will be valuable for their application in on-chip electrical interconnects. The thermal conductivity of sub-20 nm graphene ribbons is found to be more than 1000 W/m-K.

Abstract:
Post-traumatic stress disorder (PTSD) symptoms include behavioral avoidance which is acquired and tends to increase with time. This avoidance may represent a general learning bias; indeed, individuals with PTSD are often faster than controls on acquiring conditioned responses based on physiologically-aversive feedback. However, it is not clear whether this learning bias extends to cognitive feedback, or to learning from both reward and punishment. Here, male veterans with self-reported current, severe PTSD symptoms (PTSS group) or with few or no PTSD symptoms (control group) completed a probabilistic classification task that included both reward-based and punishment-based trials, where feedback could take the form of reward, punishment, or an ambiguous “no-feedback” outcome that could signal either successful avoidance of punishment or failure to obtain reward. The PTSS group outperformed the control group in total points obtained; the PTSS group specifically performed better than the control group on reward-based trials, with no difference on punishment-based trials. To better understand possible mechanisms underlying observed performance, we used a reinforcement learning model of the task, and applied maximum likelihood estimation techniques to derive estimated parameters describing individual participants’ behavior. Estimations of the reinforcement value of the no-feedback outcome were significantly greater in the control group than the PTSS group, suggesting that the control group was more likely to value this outcome as positively reinforcing (i.e., signaling successful avoidance of punishment). This is consistent with the control group’s generally poorer performance on reward trials, where reward feedback was to be obtained in preference to the no-feedback outcome. Differences in the interpretation of ambiguous feedback may contribute to the facilitated reinforcement learning often observed in PTSD patients, and may in turn provide new insight into how pathological behaviors are acquired and maintained in PTSD.

Abstract:
In order to understand the nonlinear stability of many types of time-periodic travelling waves on unbounded domains, one must overcome two main difficulties: the presence of embedded neutral eigenvalues and the time-dependence of the associated linear operator. This problem is studied in the context of time-periodic Lax shocks in systems of viscous conservation laws. Using spatial dynamics and a decomposition into separate Floquet eigenmodes, it is shown that the linear evolution for the time-dependent operator can be represented using a contour integral similar to that of the standard time-independent case. By decomposing the resulting Green's distribution, the leading order behavior associated with the embedded eigenvalues is extracted. Sharp pointwise bounds are then obtained, which are used to prove that time-periodic Lax shocks are linearly and nonlinearly stable under the necessary conditions of spectral stability and minimal multiplicity of the translational eigenvalues. The latter conditions hold, for example, for small-oscillation time-periodic waves that emerge through a supercritical Hopf bifurcation from a family of time-independent Lax shocks of possibly large amplitude.

Abstract:
A \emph{quasi-polynomial} is a function defined of the form $q(k) = c_d(k) k^d + c_{d-1}(k) k^{d-1} + ... + c_0(k)$, where $c_0, c_1, ..., c_d$ are periodic functions in $k \in \Z$. Prominent examples of quasi-polynomials appear in Ehrhart's theory as integer-point counting functions for rational polytopes, and McMullen gives upper bounds for the periods of the $c_j(k)$ for Ehrhart quasi-polynomials. For generic polytopes, McMullen's bounds seem to be sharp, but sometimes smaller periods exist. We prove that the second leading coefficient of an Ehrhart quasi-polynomial always has maximal expected period and present a general theorem that yields maximal periods for the coefficients of certain quasi-polynomials. We present a construction for (Ehrhart) quasi-polynomials that exhibit maximal period behavior and use it to answer a question of Zaslavsky on convolutions of quasi-polynomials.

Abstract:
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources which are coherent structures for which the group velocities in the far field point away from the core. Sources actively select wave numbers and therefore often organize the overall dynamics in a spatially extended system. Determining their nonlinear stability properties is challenging as localized perturbations may lead to a non-localized response even on the linear level due to the outward transport. Using a modified Burgers equation as a model problem that captures some of the essential features of coherent structures, we show how this phenomenon can be analysed and nonlinear stability be established in this simpler context.

Abstract:
In an appropriate moving coordinate frame, source defects are time-periodic solutions to reaction-diffusion equations that are spatially asymptotic to spatially periodic wave trains whose group velocities point away from the core of the defect. In this paper, we rigorously establish nonlinear stability of spectrally stable source defects in the complex Ginzburg-Landau equation. Due to the outward transport at the far field, localized perturbations may lead to a highly non-localized response even on the linear level. To overcome this, we first investigate in detail the dynamics of the solution to the linearized equation. This allows us to determine an approximate solution that satisfies the full equation up to and including quadratic terms in the nonlinearity. This approximation utilizes the fact that the non-localized phase response, resulting from the embedded zero eigenvalues, can be captured, to leading order, by the nonlinear Burgers equation. The analysis is completed by obtaining detailed estimates for the resolvent kernel and pointwise estimates for the Green's function, which allow one to close a nonlinear iteration scheme.

Abstract:
We present a multigrid scheme for the solution of finite-element Hartree-Fock equations for diatomic molecules. It is shown to be fast and accurate, the time effort depending linearly on the number of variables. Results are given for the molecules LiH, BH, N_2 and for the Be atom in our molecular grid which agrees very well with accurate values from an atomic code. Highest accuracies were obtained by applying an extrapolation scheme; we compare with other numerical methods. For N_2 we get an accuracy below 1 nHartree.

Abstract:
The measurement of parity violation in the helicity dependence of electron-nucleon scattering provides unique information about the basic quark structure of the nucleons. In this review, the general formalism of parity-violating electron scattering is presented, with emphasis on elastic electron-nucleon scattering. The physics issues addressed by such experiments is discussed, and the major goals of the presently envisioned experimental program are identified. %General aspects of the experimental technique are reviewed and A summary of results from a recent series of experiments is presented and the future prospects of this program are also discussed.

Abstract:
The magnetic field of galaxies is believed to be produced by internal dynamo action, but can be affected by motion of the galaxy through the surrounding medium. Observations of polarized radio emission of galaxies located in galaxy clusters have revealed noticeable features of large-scale magnetic configurations, including displacements of the magnetic structures from the optical images and tails, which are possible imprints of ram pressure effects arising from motion of the galaxies through the intracluster medium. We present a quantitative dynamo model which attempts to describe the above effects. In contrast to the traditional problem of a wind affecting a body with a prescribed magnetic field, we investigate how a non-magnetized wind flow affects a magnetic field that is being self-excited by galactic dynamo action. In order to isolate the leading physical effects we exploit a simple dynamo model that can describe relevant effects. In particular, we use what is known as the 'no-z' approximation for the mean-field dynamo equations. In a suitable parametric range we obtain displacements of the large-scale magnetic field, as well as magnetic tails. However, the specific details of their locations are quite counterintuitive. The direction of displacement is perpendicular to, rather than parallel to, the wind direction. The point at which the tail emerges from the galaxy depends on details of the model. The tail is eventually directed downstream. In the simplest case the magnetic tail begins in the region where the wind decreases the total gas velocity. Any wind that penetrates the galaxy modifies the intrinsic dynamo action. These features are different from those found in ram-pressure models. Any determination of galactic motion through the cluster medium from observational data needs to take the effects of dynamo action into account.