Dynamics of Annealed Systems under External Fields: CTRW and the Fractional Fokker-Planck Equations

We consider the linear response of a system modelled by continuous-time random walks (CTRW) to an external field pulse of rectangular shape. We calculate the corresponding response function explicitely and show that it exhibits aging, i.e. that it is not translationally invariant in the time-domain. This result differs from that of systems which behave according to fractional Fokker-Planck equations

Quantum walk approach to search on fractal structures

We study continuous-time quantum walks mimicking the quantum search based on Grover's procedure. This allows us to consider structures, that is, databases, with arbitrary topological arrangements of their entries. We show that the topological structure of the database plays a crucial role by analyzing, both analytically and numerically, the transition from the ground to the first excited state of the Hamiltonian associated with different (fractal) structures. Additionally, we use the probability of successfully finding a specific target as another indicator of the importance of the topological structure.Comment: 15 pages, 14 figure

Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks

In this work we investigate the spectra of Laplacian matrices that determine many dynamic properties of scale-free networks below and at the percolation threshold. We use a replica formalism to develop analytically, based on an integral equation, a systematic way to determine the ensemble averaged eigenvalue spectrum for a general type of tree-like networks. Close to the percolation threshold we find characteristic scaling functions for the density of states rho(lambda) of scale-free networks. rho(lambda) shows characteristic power laws rho(lambda) ~ lambda^alpha_1 or rho(lambda) ~ lambda^alpha_2 for small lambda, where alpha_1 holds below and alpha_2 at the percolation threshold. In the range where the spectra are accessible from a numerical diagonalization procedure the two methods lead to very similar results.Comment: 9 pages, 6 figure

Space Fortress Game Training and Executive Control in Older Adults: A Pilot Intervention

We investigated the feasibility of using the Space Fortress (SF) game, a complex video game originally developed to study complex skill acquisition in young adults, to improve executive control processes in cognitively healthy older adults. The study protocol consisted of 36 one-hour game play sessions over 3 months with cognitive evaluations before and after, and a follow-up evaluation at 6 months. Sixty participants were randomized to one of three conditions: Emphasis Change (EC)--elders were instructed to concentrate on playing the entire game but place particular emphasis on a specific aspect of game play in each particular game; Active Control (AC)--game play with standard instructions; Passive Control (PC)--evaluation sessions without game play. Primary outcome measures were obtained from five tasks, presumably tapping executive control processes. A total of 54 older adults completed the study protocol. One measure of executive control, WAIS-III letter-number sequencing, showed improvement in performance from pre- to post-evaluations in the EC condition, but not in the other two conditions. These initial findings are modest but encouraging. Future SF interventions need to carefully consider increasing the duration and or the intensity of the intervention by providing at-home game training, reducing the motor demands of the game, and selecting appropriate outcome measures

Lie theory and separation of variables. 5. The equations iUt + Uxx = 0 and iUt + Uxx −c/x2 U = 0

A detailed study of the group of symmetries of the time-dependent free particle Schrödinger equation in one space dimension is presented. An orbit analysis of all first order symmetries is seen to correspond in a well-defined manner to the separation of variables of this equation. The study gives a unified treatment of the harmonic oscillator (both attractive and repulsive), Stark effect, and free particle Hamiltonians in the time dependent formalism. The case of a potential c/x2 is also discussed in the time dependent formalism. Use of representation theory for the symmetry groups permits simple derivation of expansions relating various solutions of the Schrödinger equation, several of which are new

Assessing phytoplankton nutritional status and potential impact of wet deposition in seasonally oligotrophic waters of the Mid‐Atlantic Bight

Author Posting. © American Geophysical Union, 2018. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 45 (2018): 3203-3211, doi:10.1002/2017GL075361.To assess phytoplankton nutritional status in seasonally oligotrophic waters of the southern Mid‐Atlantic Bight, and the potential for rain to stimulate primary production in this region during summer, shipboard bioassay experiments were performed using natural seawater and phytoplankton collected north and south of the Gulf Stream. Bioassay treatments comprised iron, nitrate, iron + nitrate, iron + nitrate + phosphate, and rainwater. Phytoplankton growth was inferred from changes in chlorophyll a, inorganic nitrogen, and carbon‐13 uptake, relative to unamended control treatments. Results indicated the greatest growth stimulation by iron + nitrate + phosphate, intermediate growth stimulation by rainwater, modest growth stimulation by nitrate and iron + nitrate, and no growth stimulation by iron. Based on these data and analysis of seawater and atmospheric samples, nitrogen was the proximate limiting nutrient, with a secondary limitation imposed by phosphorus. Our results imply that summer rain events increase new production in these waters by contributing nitrogen and phosphorus, with the availability of the latter setting the upper limit on rain‐stimulated new production.US National Science Foundation Grant Numbers: OCE‐1260454, OCE‐1260454, OCE‐12605742018-09-1