Minimal surfaces from circle patterns: Geometry from combinatorics

We suggest a new definition for discrete minimal surfaces in terms of sphere packings with orthogonally intersecting circles. These discrete minimal surfaces can be constructed from Schramm's circle patterns. We present a variational principle which allows us to construct discrete analogues of some classical minimal surfaces. The data used for the construction are purely combinatorial--the combinatorics of the curvature line pattern. A Weierstrass-type representation and an associated family are derived. We show the convergence to continuous minimal surfaces.Comment: 30 pages, many figures, some in reduced resolution. v2: Extended introduction. Minor changes in presentation. v3: revision according to the referee's suggestions, improved & expanded exposition, references added, minor mistakes correcte

A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow

Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time simulation of smoke. Here we introduce a time-discrete evolution equation for arbitrary closed polygons in 3-space that is a discretisation of the localised induction approximation of filament motion. This discretisation shares with its continuum limit the property that it is a completely integrable system. We apply this polygon evolution to a significant improvement of the numerical algorithms used in Computer Graphics.Comment: 15 pages, 3 figure

Long-term in vivo imaging of fibrillar tau in the retina of P301S transgenic mice.

Tauopathies are widespread neurodegenerative disorders characterised by the intracellular accumulation of hyperphosphorylated tau. Especially in Alzheimer's disease, pathological alterations in the retina are discussed as potential biomarkers to improve early diagnosis of the disease. Using mice expressing human mutant P301S tau, we demonstrate for the first time a straightforward optical approach for the in vivo detection of fibrillar tau in the retina. Longitudinal examinations of individual animals revealed the fate of single cells containing fibrillar tau and the progression of tau pathology over several months. This technique is most suitable to monitor therapeutic interventions aimed at reducing the accumulation of fibrillar tau. In order to evaluate if this approach can be translated to human diagnosis, we tried to detect fibrillar protein aggregates in the post-mortem retinas of patients that had suffered from Alzheimer's disease or Progressive Supranuclear Palsy. Even though we could detect hyperphosphorylated tau, we did not observe any fibrillar tau or Aß aggregates. In contradiction to previous studies, our observations do not support the notion that Aβ or tau in the retina are of diagnostic value in Alzheimer's disease

Lithium Dendrite Inhibition on Post-Charge Anode Surface: The Kinetics Role

We report experiments and molecular dynamics calculations on the kinetics of electrodeposited lithium dendrites relaxation as a function of temperature and time. We found that the experimental average length of dendrite population decays via stretched exponential functions of time toward limiting values that depend inversely on temperature. The experimental activation energy derived from initial rates as E_a~ 6-7 kcal/mole, which is closely matched by MD calculations, based on the ReaxFF force field for metallic lithium. Simulations reveal that relaxation proceeds in several steps via increasingly larger activation barriers. Incomplete relaxation at lower temperatures is therefore interpreted a manifestation of cooperative atomic motions into discrete topologies that frustrate monotonic progress by ‘caging’

Dynamics of Lithium Dendrite Growth and Inhibition: Pulse Charging Experiments and Monte Carlo Calculations

Short-circuiting via dendrites compromises the reliability of Li-metal batteries. Dendrites ensue from instabilities inherent to electrodeposition that should be amenable to dynamic control. Here, we report that by charging a scaled coin-cell prototype with 1 ms pulses followed by 3 ms rest periods the average dendrite length is shortened ~2.5 times relative to those grown under continuous charging. Monte Carlo simulations dealing with Li^+ diffusion and electromigration reveal that experiments involving 20 ms pulses were ineffective because Li^+ migration in the strong electric fields converging to dendrite tips generates extended depleted layers that cannot be replenished by diffusion during rest periods. Because the application of pulses much shorter than the characteristic time τ_c~O(1 ms) for polarizing electric double layers in our system would approach DC charging, we suggest that dendrite propagation can be inhibited (albeit not suppressed) by pulse charging within appropriate frequency ranges

Ion stopping in dense plasma target for high energy density physics

The basic physics of nonrelativistic and electromagnetic ion stopping in hot and ionized plasma targets is thoroughly updated. Corresponding projectile-target interactions involve enhanced projectile ionization and coupling with target free electrons leading to significantly larger energy losses in hot targets when contrasted to their cold homologues. Standard stoppping formalism is framed around the most economical extrapolation of high velocity stopping in cold matter. Further elaborations pay attention to target electron coupling and nonlinearities due to enhanced projectile charge state, as well. Scaling rules are then used to optimize the enhanced stopping of MeV/amu ions in plasmas with electron linear densities nel ~ 10 18 -10 20 cm -2 . The synchronous firing of dense and strongly ionized plasmas with the time structure of bunched and energetic multicharged ion beam then allow to probe, for the first time, the long searched enhanced plasma stopping and projectile charge at target exit. Laser ablated plasmas (SPQR1) and dense linear plasma columns (SPQR2) show up as targets of choice in providing accurate and on line measurements of plasma parameters. Corresponding stopping results are of a central significance in asserting the validity of intense ion beam scenarios for driving thermonuclear pellets. Other applications of note feature thorium induced fission, novel ion sources and specific material processing through low energy ion beams. Last but not least, the given ion beam-plasma target interaction physics is likely to pave a way to the production and diagnostics of warm dense matter (WDM)

Local Electrical Dyssynchrony during Atrial Fibrillation: Theoretical Considerations and Initial Catheter Ablation Results

Copyright: © 2016 Kuklik et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Background Electrogram-based identification of the regions maintaining persistent Atrial Fibrillation (AF) is a subject of ongoing debate. Here, we explore the concept of local electrical dyssynchrony to identify AF drivers. Methods and Results Local electrical dyssynchrony was calculated using mean phase coherence. High-density epicardial mapping along with mathematical model were used to explore the link between local dyssynchrony and properties of wave conduction. High-density mapping showed a positive correlation between the dyssynchrony and number of fibrillatory waves (R2 = 0.68, p<0.001). In the mathematical model, virtual ablation at high dyssynchrony regions resulted in conduction regularization. The clinical study consisted of eighteen patients undergoing catheter ablation of persistent AF. High-density maps of left atrial (LA) were constructed using a circular mapping catheter. After pulmonary vein isolation, regions with the top 10% of the highest dyssynchrony in LA were targeted during ablation and followed with ablation of complex atrial electrograms. Catheter ablation resulted in termination during ablation at high dyssynchrony regions in 7 (41%) patients. In another 4 (24%) patients, transient organization was observed. In 6 (35%) there was no clear effect. Long-term follow-up showed 65% AF freedom at 1 year and 22% at 2 years. Conclusions Local electrical dyssynchrony provides a reasonable estimator of regional AF complexity defined as the number of fibrillatory waves. Additionally, it points to regions of dynamical instability related with action potential alternans. However, despite those characteristics, its utility in guiding catheter ablation of AF is limited suggesting other factors are responsible for AF persistence

Thermal relaxation of lithium dendrites

The average lengths λ^- of lithium dendrites produced by charging symmetric Li^0 batteries at various temperatures are matched by Monte Carlo computations dealing both with Li^+ transport in the electrolyte and thermal relaxation of Li0 electrodeposits. We found that experimental λ^-(T) variations cannot be solely accounted by the temperature dependence of Li^+ mobility in the solvent but require the involvement of competitive Li-atom transport from metastable dendrite tips to smoother domains over ΔE^(‡)_R ~ 20 kJ mol^−1 barriers. A transition state theory analysis of Li-atom diffusion in solids yields a negative entropy of activation for the relaxation process: ΔS^(‡)_R ≈ −46 J mol^−1 K^−1 that is consistent with the transformation of amorphous into crystalline Li0 electrodeposits. Significantly, our ΔE^(‡)R ~ 20 kJ mol^−1 value compares favorably with the activation barriers recently derived from DFT calculations for self-diffusion on Li^0(001) and (111) crystal surfaces. Our findings suggest a key role for the mobility of interfacial Li-atoms in determining the morphology of dendrites at temperatures above the onset of surface reconstruction: TSR ≈ 0.65 T_MB (T_MB = 453 K: the melting point of bulk Li^0)