Dynamic percolation theory for particle diffusion in a polymer network

Tracer-diffusion of small molecules through dense systems of chain polymers is studied within an athermal lattice model, where hard core interactions are taken into account by means of the site exclusion principle. An approximate mapping of this problem onto dynamic percolation theory is proposed. This method is shown to yield quantitative results for the tracer correlation factor of the molecules as a function of density and chain length provided the non-Poisson character of temporal renewals in the disorder configurations is properly taken into account

Capture numbers and islands size distributions in models of submonolayer surface growth

The capture numbers entering the rate equations (RE) for submonolayer film growth are determined from extensive kinetic Monte Carlo (KMC) simulations for simple representative growth models yielding point, compact, and fractal island morphologies. The full dependence of the capture numbers on island size, and on both the coverage and the D/F ratio between the adatom diffusion coefficient D and deposition rate F is determined. Based on this information, the RE are solved to give the RE island size distribution (RE-ISD). The RE-ISDs are shown to agree well with the corresponding KMC-ISDs for all island morphologies. For compact morphologies, however, this agreement is only present for coverages smaller than about 5% due to a significantly increased coalescence rate compared to fractal morphologies. As found earlier, the scaled KMC-ISDs as a function of scaled island size approach, for fixed coverage, a limiting curve for D/F going to infinity. Our findings provide evidence that the limiting curve is independent of the coverage for point islands, while the results for compact and fractal island morphologies indicate a dependence on the coverage.Comment: 13 pages, 12 figure

Loss of control in pattern-directed nucleation: a theoretical study

The properties of template-directed nucleation are studied close to the transition where full nucleation control is lost and additional nucleation occurs beyond the pre-patterned regions. First, kinetic Monte Carlo simulations are performed to obtain information on a microscopic level. Here the experimentally relevant cases of 1D stripe patterns and 2D square lattice symmetry are considered. The nucleation properties in the transition region depend in a complex way on the parameters of the system, i.e. the flux, the surface diffusion constant, the geometric properties of the pattern and the desorption rate. Second, the properties of the stationary concentration field in the fully controlled case are studied to derive the remaining nucleation probability and thus to characterize the loss of nucleation control. Using the analytically accessible solution of a model system with purely radial symmetry, some of the observed properties can be rationalized. A detailed comparison to the Monte Carlo data is included

Rate- and State-Dependent Friction Law and Statistical Properties of Earthquakes

In order to clarify how the statistical properties of earthquakes depend on the constitutive law characterizing the stick-slip dynamics, we make an extensive numerical simulation of the one-dimensional spring-block model with the rate- and state-dependent friction law. Both the magnitude distribution and the recurrence-time distribution are studied with varying the constitutive parameters characterizing the model. While a continuous spectrum of seismic events from smaller to larger magnitudes is obtained, earthquakes described by this model turn out to possess pronounced ``characteristic'' features.Comment: Minor revisions are made in the text and in the figures. Accepted for publication in Europhys. Letter

Shape configuration of mental targets representation as a holistic measure in a 3D real world pointing test for spatial orientation

Deficits in spatial memory are often early signs of neurological disorders. Here, we analyzed the geometrical shape configuration of 2D-projections of pointing performances to a memorized array of spatially distributed targets in order to assess the feasibility of this new holistic analysis method. The influence of gender differences and cognitive impairment was taken into account in this methodological study. 56 right-handed healthy participants (28 female, mean age 48.89 +/- 19.35 years) and 22 right-handed patients with heterogeneous cognitive impairment (12 female, mean age 71.73 +/- 7.41 years) underwent a previously validated 3D-real-world pointing test (3D-RWPT). Participants were shown a 9-dot target matrix and afterwards asked to point towards each target in randomized order with closed eyes in different body positions relative to the matrix. Two-dimensional projections of these pointing vectors (i.e., the shapes resulting from the individual dots) were then quantified using morphological analyses. Shape configurations in healthy volunteers largely reflected the real-world target pattern with gender-dependent differences (ANCOVA area males vs. females F(1,73) = 9.00, p 3.69 x 10-3, partial eta 2 = 0.10, post-hoc difference = 38,350.43, pbonf=3.69 x 10-3**, Cohen's d 0.76, t 3.00). Patients with cognitive impairment showed distorted rectangularity with more large-scale errors, resulting in decreased overall average diameters and solidity (ANCOVA diameter normal cognition/cognitive impairment F(1,71) = 9.30, p 3.22 x 10-3, partial eta 2 = 0.09, post-hoc difference = 31.22, pbonf=3.19 x 10-3**, Cohen's d 0.92, t 3.05;solidity normal cognition/cognitive impairment F(1,71) = 7.79, p 6.75 x 10-3, partial eta 2 = 0.08, post-hoc difference = 0.07, pbonf=6.76 x 10-3** Cohen's d 0.84, t 2.79). Shape configuration analysis of the 3D-RWPT target array appears to be a suitable holistic measure of spatial performance in a pointing task. The results of this methodological investigation support further testing in a clinical study for differential diagnosis of disorders with spatial memory deficits

A clinical 3D pointing test differentiates spatial memory deficits in dementia and bilateral vestibular failure

Background Deficits in spatial memory, orientation, and navigation are often neglected early signs of cognitive impairment or loss of vestibular function. Real-world navigation tests require complex setups. In contrast, simple pointing at targets in a three-dimensional environment is a basic sensorimotor ability which provides an alternative measure of spatial orientation and memory at bedside. The aim of this study was to test the reliability of a previously established 3D-Real-World Pointing Test (3D-RWPT) in patients with cognitive impairment due to different neurodegenerative disorders, bilateral vestibulopathy, or a combination of both compared to healthy participants. Methods The 3D-RWPT was performed using a static array of targets in front of the seated participant before and, as a transformation task, after a 90-degree body rotation around the yaw-axis. Three groups of patients were enrolled: (1) chronic bilateral vestibulopathy (BVP) with normal cognition (n = 32), (2) cognitive impairment with normal vestibular function (n = 28), and (3) combined BVP and cognitive impairment (n = 9). The control group consisted of age-matched participants (HP) without cognitive and vestibular deficits (n = 67). Analyses focused on paradigm-specific mean angular deviation of pointing in the azimuth (horizontal) and polar (vertical) spatial planes, of the preferred pointing strategy (egocentric or allocentric), and the resulting shape configuration of the pointing array relative to the stimulus array. Statistical analysis was performed using age-corrected ANCOVA-testing with Bonferroni correction and correlation analysis using Spearman's rho. Results Patients with cognitive impairment employed more egocentric pointing strategies while patients with BVP but normal cognition and HP used more world-based solutions (pBonf 5.78 x 10-3**). Differences in pointing accuracy were only found in the azimuth plane, unveiling unique patterns where patients with cognitive impairment showed decreased accuracy in the transformation tasks of the 3D-RWPT (pBonf < 0.001***) while patients with BVP struggled in the post-rotation tasks (pBonf < 0.001***). Overall azimuth pointing performance was still adequate in some patients with BVP but significantly decreased when combined with a cognitive deficit. Conclusion The 3D-RWPT provides a simple and fast measure of spatial orientation and memory. Cognitive impairment often led to a shift from world-based allocentric pointing strategy to an egocentric performance with less azimuth accuracy compared to age-matched controls. This supports the view that cognitive deficits hinder the mental buildup of the stimulus pattern represented as a geometrical form. Vestibular hypofunction negatively affected spatial memory and pointing performance in the azimuth plane. The most severe spatial impairments (angular deviation, figure frame configuration) were found in patients with combined cognitive and vestibular deficits

Influence of external magnetic fields on growth of alloy nanoclusters

Kinetic Monte Carlo simulations are performed to study the influence of external magnetic fields on the growth of magnetic fcc binary alloy nanoclusters with perpendicular magnetic anisotropy. The underlying kinetic model is designed to describe essential structural and magnetic properties of CoPt_3-type clusters grown on a weakly interacting substrate through molecular beam epitaxy. The results suggest that perpendicular magnetic anisotropy can be enhanced when the field is applied during growth. For equilibrium bulk systems a significant shift of the onset temperature for L1_2 ordering is found, in agreement with predictions from Landau theory. Stronger field induced effects can be expected for magnetic fcc-alloys undergoing L1_0 ordering.Comment: 10 pages, 3 figure

On the Backbending Mechanism of 48^{48}Cr

The mechanism of backbending in $^{48}$Cr is investigated in terms of the Projected Shell Model and the Generator Coordinate Method. It is shown that both methods are reasonable shell model truncation schemes. These two quite different quantum mechanical approaches lead to a similar conclusion that the backbending is due to a band crossing involving an excited band which is built on simultaneously broken neutron and proton pairs in the ``intruder'' subshell $f_{7/2}$. It is pointed out that this type of band crossing is usually known to cause the second backbending in rare-earth nuclei.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Let

ASK/PSK-correspondence and the r-map

We formulate a correspondence between affine and projective special K\"ahler manifolds of the same dimension. As an application, we show that, under this correspondence, the affine special K\"ahler manifolds in the image of the rigid r-map are mapped to one-parameter deformations of projective special K\"ahler manifolds in the image of the supergravity r-map. The above one-parameter deformations are interpreted as perturbative $\alpha'$-corrections in heterotic and type-II string compactifications with $N=2$ supersymmetry. Also affine special K\"ahler manifolds with quadratic prepotential are mapped to one-parameter families of projective special K\"ahler manifolds with quadratic prepotential. We show that the completeness of the deformed supergravity r-map metric depends solely on the (well-understood) completeness of the undeformed metric and the sign of the deformation parameter