Collective Diffusion and a Random Energy Landscape

Starting from a master equation in a quantum Hamiltonian form and a coupling to a heat bath we derive an evolution equation for a collective hopping process under the influence of a stochastic energy landscape. There results different equations in case of an arbitrary occupation number per lattice site or in a system under exclusion. Based on scaling arguments it will be demonstrated that both systems belong below the critical dimension $d_c$ to the same universality class leading to anomalous diffusion in the long time limit. The dynamical exponent $z$ can be calculated by an $\epsilon = d_c-d$ expansion. Above the critical dimension we discuss the differences in the diffusion constant for sufficient high temperatures. For a random potential we find a higher mobility for systems with exclusion.Comment: 15 pages, no figure

InP-quantum dots in Al0.20Ga0.80InP with different barrier configurations

Systematic ensemble photoluminescence studies have been performed on type-I InP-quantum dots in Al0.20Ga0.80InP barriers, emitting at approximately 1.85 eV at 5 K. The influence of different barrier configurations as well as the incorporation of additional tunnel barriers on the optical properties has been investigated. The confinement energy between the dot barrier and the surrounding barrier layers, which is the sum of the band discontinuities for the valence and the conduction bands, was chosen to be approximately 190 meV by using Al0.50Ga0.50InP. In combination with 2 nm thick AlInP tunnel barriers, the internal quantum efficiency of these barrier configurations can be increased by up to a factor of 20 at elevated temperatures with respect to quantum dots without such layers.Comment: physica status solidi (c) (Proceedings of QD 2008

Ion radial diffusion in an electrostatic impulse model for stormtime ring current formation

Guiding-center simulations of stormtime transport of ring-current and radiation-belt ions having first adiabatic invariants mu is approximately greater than 15 MeV/G (E is approximately greater than 165 keV at L is approximately 3) are surprisingly well described (typically within a factor of approximately less than 4) by the quasilinear theory of radial diffusion. This holds even for the case of an individual model storm characterized by substorm-associated impulses in the convection electric field, provided that the actual spectrum of the electric field is incorporated in the quasilinear theory. Correction of the quasilinear diffusion coefficient D(sub LL)(sup ql) for drift-resonance broadening (so as to define D(sub LL)(sup ql)) reduced the typical discrepancy with the diffusion coefficients D(sub LL)(sup sim) deduced from guiding-center simulations of representative-particle trajectories to a factor of approximately 3. The typical discrepancy was reduced to a factor of approximately 1.4 by averaging D(sub LL)(sup sim), D(sub LL)(sup ql), and D(sub LL)(sup rb) over an ensemble of model storms characterized by different (but statistically equivalent) sets of substorm-onset times

Calcification depth of deep-dwelling planktonic foraminifera from the eastern North Atlantic constrained by stable oxygen isotope ratios of shells from stratified plankton tows

Stable oxygen isotopes (delta O-18) of planktonic foraminifera are one of the most used tools to reconstruct environmental conditions of the water column. Since different species live and calcify at different depths in the water column, the delta O-18 of sedimentary foraminifera reflects to a large degree the vertical habitat and interspecies delta O-18 differences and can thus potentially provide information on the vertical structure of the water column. However, to fully unlock the potential of foraminifera as recorders of past surface water properties, it is necessary to understand how and under what conditions the environmental signal is incorporated into the calcite shells of individual species. Deep-dwelling species play a particularly important role in this context since their calcification depth reaches below the surface mixed layer. Here we report delta O-18 measurements made on four deep-dwelling Globorotalia species collected with stratified plankton tows in the eastern North Atlantic. Size and crust effects on the delta O-18 signal were evaluated showing that a larger size increases the delta O-18 of G. inflata and G. hirsuta, and a crust effect is reflected in a higher delta O-18 signal in G. truncatulinoides. The great majority of the delta O-18 values can be explained without invoking disequilibrium calcification. When interpreted in this way the data imply depth-integrated calcification with progressive addition of calcite with depth to about 300m for G. inflata and to about 500m for G. hirsuta. In G. scitula, despite a strong subsurface maximum in abundance, the vertical delta O-18 profile is flat and appears dominated by a surface layer signal. In G. truncatulinoides, the delta O-18 profile follows equilibrium for each depth, implying a constant habitat during growth at each depth layer. The delta O-18 values are more consistent with the predictions of the Shackleton (1974) palaeotemperature equation, except in G. scitula which shows values more consistent with the Kim and O'Neil (1997) prediction. In all cases, we observe a difference between the level where most of the specimens were present and the depth where most of their shell appears to calcify.Agência financiadora Portuguese Foundation for Science and Technology (FCT): SFRH/BD/78016/2011; UID/Multi/04326/2019 European Union Seventh Framework Programme (FP7/2007-2013): 228344-EUROFLEETS German Research Foundation (DFG): WA2175/2-1; WA2175/4-1 German Climate Modelling consortium PalMod - German Federal Ministry of Education and Research (BMBF)info:eu-repo/semantics/publishedVersio

Geometric limits of Mandelbrot and Julia sets under degree growth

First, for the family P_{n,c}(z) = z^n + c, we show that the geometric limit of the Mandelbrot sets M_n(P) as n tends to infinity exists and is the closed unit disk, and that the geometric limit of the Julia sets J(P_{n,c}) as n tends to infinity is the unit circle, at least when the modulus of c is not one. Then we establish similar results for some generalizations of this family; namely, the maps F_{t,c} (z) = z^t+c for real t>= 2, and the rational maps R_{n,c,a} (z) = z^n + c + a/z^n.Comment: 29 pages, 16 figures (34 pic files), submitte

Differential Double Capture Cross Sections in P+He Collisions

We have measured differential double capture cross sections for 15 to 150 keV p+He collisions. We also analyzed differential double to single capture ratios, where we find pronounced peak structures. An explanation of these structures probably requires a quantum-mechanical description of elastic scattering between the projectile and the target nucleus. Strong final-state correlations have a large effect on the magnitude of the double capture cross section

Characterizing Simultaneous Embeddings with Fixed Edges

A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V in the plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same Jordan curve in the simultaneous drawings. While any number of planar graphs have a simultaneous embedding without fixed edges, determining which graphs always share a simultaneous embedding with fixed edges (SEFE) has been open. We partially close this problem by giving a necessary condition to determine when pairs of graphs have a SEFE

Characterizations of Restricted Pairs of Planar Graphs allowing Simultaneous Embeddings with Fixed Edges

A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V in the Euclidean plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same simple curve in the simultaneous drawing. Determining in polynomial time which pairs of graphs share a simultaneous embedding with ?xed edges (SEFE) has been open. We give a necessary and su?cient condition for whether a SEFE exists for pairs of graphs whose union is homeomorphic to K5 or K3,3 . This allows us to characterize the class of planar graphs that always have a SEFE with any other planar graph. We also characterize the class of biconnected outerplanar graphs that always have a SEFE with any other outerplanar graph. In both cases, we provide e?cient algorithms to compute a SEFE. Finally, we provide a linear-time decision algorithm for deciding whether a pair of biconnected outerplanar graphs has a SEFE

Characterizing Simultaneous Embeddings with Fixed Edges

A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V in the plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same Jordan curve in the simultaneous drawings. While any number of planar graphs have a simultaneous embedding without ?xed edges, determining which graphs always share a simultaneous embedding with ?xed edges (SEFE) has been open. We partially close this problem by giving a necessary condition to determine when pairs of graphs have a SEFE

An SPQR-Tree Approach to Decide Special Cases of Simultaneous Embedding with Fixed Edges

We present a linear-time algorithm for solving the simulta- neous embedding problem with ?xed edges (SEFE) for a planar graph and a pseudoforest (a graph with at most one cycle) by reducing it to the following embedding problem: Given a planar graph G, a cycle C of G, and a partitioning of the remaining vertices of G, does there exist a planar embedding in which the induced subgraph on each vertex partite of G C is contained entirely inside or outside C ? For the latter prob- lem, we present an algorithm that is based on SPQR-trees and has linear running time. We also show how we can employ SPQR-trees to decide SEFE for two planar graphs where one graph has at most two cycles and the intersection is a pseudoforest in linear time. These results give rise to our hope that our SPQR-tree approach might eventually lead to a polynomial-time algorithm for deciding the general SEFE problem for two planar graphs