Exploring the performance of spatial stochastic simulation algorithms

Since the publication of Gillespie’s direct method, diverse methods have been developed to improve the performance of stochastic simulation methods and to enter the spatial realm. In this paper we discuss a spatial τ-leaping variant (Sτ) that extends the basic leap method. Sτ takes reaction and both outgoing and incoming diffusion events into account when calculating a leap candidate. A performance analysis shall reveal details on the achieved success in balancing speed and accuracy in comparison to other methods. However, performance analysis of spatial stochastic algorithms requires significant effort — it is crucial to choose suitable (benchmark) models and to carefully define model and simulation setups that take problem and simulation design spaces into account.     

FT Raman investigation of sodium cellulose sulfate

FT Raman investigation of sodium cellulose sulfates (NaCS) was reported. Different NaCS were prepared by two diverse sulfation methods and their total degrees of substitution (DS) of sulfate groups were determined through either ¹³C-NMR spectroscopy or elemental analysis. Subsequently, these NaCS were characterized with FT Raman spectroscopy. The caused bands through the introduction of the sulfate groups in cellulose chain were explained and assigned. Additionally, a strong linear correlation between the areas under the bands ascribed to the stretching vibrations of C–O–S groups and the total DS of NaCS was presented. A rapid method of quantifying the total DS of NaCS was established. Finally, sodium sulfate (Na₂SO₄), a salt that is very often produced during the sulfation of cellulose, was found to be analyzable even with a weight content of 0.12% in NaCS. The method of quantifying the content of this salt in NaCS was investigated with Raman spectroscopy.     

Continuity of the SLE trace in simply connected domains

We prove that the SLE _κ trace in any simply connected domain G is continuous (except possibly near its endpoints) if κ < 8. We also prove an SLE analog of Makarov’s Theorem about the support of harmonic measure.     

The Susceptibility of Non-UV Fluorescent Membrane Dyes to Dynamical Properties of Lipid Membranes

Fluorescence spectroscopy and microscopy are powerful techniques to detect dynamic properties in artificial and natural lipid membrane systems. Unfortunately, most fluorescent dyes that sense dynamically relevant membrane parameters are UV sensitive. Their major disadvantage is a high susceptibility to fluorescence bleaching. Additionally, the risk for hazardous damages in biological components generally increases with decreasing excitation wavelength. Therefore the use of non-UV–sensitive membrane dyes would provide significant advantage, particularly for applications in fluorescence microscopy, which usually implies high local excitation intensities. We applied steady-state fluorescence spectroscopy techniques to several UV and non-UV membrane dyes to detect and compare dynamically relevant excitation and emission characteristics. Small unilamellar liposomes (composed of egg yolk phosphatidylcholine) served as a model system for biological membranes. The dynamic properties of the membranes were varied by two independent parameters: the intrinsic cholesterol content (0–50 mol%) and temperature (10–50°C). We tested four non-UV–sensitive membrane dyes: 9-diethylamino-5H-benzophenoxazine-5-one (Nile Red), 4-(dicyanovinyl)julolidine (DCVJ), N-(3-triethylammoniumpropyl)-4-(4-(dibutylamino)styryl) pyridinium dibromide (FM 4-64), and 1,1-dioctadecyl-3,3,3,3-tetramethylindocarbocyanine perchlorate (DiIC₁₈). We also tested three derivatives of DiIC₁₈: DiIC₁₆ and DiIC₁₂ differ in acyl chain length and Fast-DiIC₁₈ provides double bonds between hydrocarbon atoms. The spectral results were compared to established fluorescence characteristics of four UV membrane dyes: the anisotropy of 1-6-phenyl-1,3,5,-hexatrien (DPH), two derivatives of DPH (TMA-DPH and COO^–-DHP), and the generalized polarization of 6-dodecanoyl-2-dimethyl-aminonaphthalene (Laurdan). Our results indicate that the tested non-UV dyes do not reveal dynamically relevant membrane parameters in a direct manner. However, spectral characteristics make DiIC₁₈, Nile Red, and DCVJ promising probes for the microscopic detection of lateral lipid organization, an indirect indicator of membrane dynamics. In particular, DiIC₁₈ showed very selective shifts in the emission spectra at defined temperatures and cholesterol contents that have not been reported elsewhere.     

Efficiency of homonuclear Hartmann-Hahn and COSY-type mixing sequences in the presence of scalar and residual dipolar couplings

In the presence of scalar (J) and residual dipolar (D) couplings, the transfer efficiency of homonuclear Hartmann-Hahn and COSY-type mixing depends on the ratio D/J and on the mixing sequence. This dependence is analyzed theoretically and the results are confirmed experimentally. At least two different mixing sequences are required to yield good transfer efficiencies for all ratios D/J. In contrast to COSY-type experiments, homonuclear Hartmann-Hahn sequences can provide efficient transfer even if the sum of D and J is zero, i.e., if the coupling vanishes in the weak coupling limit.     

Light-scattering study of a supercooled epoxy resin

The dynamics of the fragile glass-forming liquid diglycidyl ether of bisphenol-A was studied by depolarized Rayleigh-Brillouin light-scattering and photon correlation spectroscopy above the glass transition, in the temperature range from 261 to 473 K and in the frequency range from 1 Hz to 300 GHz. The structural (alpha-) relaxation process was revealed and no signature of the secondary relaxation previously evidenced by dielectric spectroscopy at about 0.1 GHz was observed. The characteristic time of the alpha process differs from that determined by dielectric spectroscopy of an amount, which increases with increasing temperature. The relaxation times were compared with viscosity data to test the predictions of the classic Stokes-Einstein-Debye model. The tau proportional, variant eta behavior was verified for dielectric data, while a fractional power law of viscosity tau proportional, variant eta(0.89) was obtained for light-scattering relaxation times, extending over more than seven decades in viscosity and time. This deviation of light scattering from viscosity data could be interpreted in terms of cooperative motion in the supercooled liquid with a characteristic length xi(a) proportional, variant(T-T0)(-v) where T(0)=229 K is the Vogel temperature and v is close to 2 / 3 which is consistent with the prediction of the fluctuation theory of glass transition.