Experiments with single atoms in cavities and traps

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Polyhedral graphs with extreme numbers of types of faces

A face F of a polyhedral graph G(V,E,F) is an a₁,a₂,…,a_l-face if is an l-gon and the degrees d(x_i) of the vertices x_iV incident with in the cyclic order are a_i,i=1,2,…,l. The lexicographic minimum b₁,b₂,…,b_l such that is a b₁,b₂,…,b_l-face is the type of . All polyhedral graphs having only one type of faces are listed. It is proved that the set of triangulations having only faces of different types is non-empty and finite.     

On a Model for Soft Landing with State-Dependent Delay

Automatic soft landing is modeled by a differential equation with state-dependent delay. It is shown that in the model soft landing occurs for an open set of initial data, which is determined by means of a smooth invariant manifold.      

Dendronized Hyperbranched Macromolecules: Soft Matter with a Novel Type of Segmental Distribution

Dendronization of a hyperbranched polyester with different generation dendrons leads to pseudo‐dendritic structures. The hyperbranched core is modified by the divergent coupling of protected monomer units to the functional groups. Compared to dendrimers, the synthetic effort is significantly less, but the properties are very close to those of high‐generation dendrimers. The number of functional groups, molar mass, and rheology behavior even in the early generation (G1–G4) pseudo‐dendrimers strongly resembles the behavior of dendrimers in higher generations (G5–G8). Comparison of the segmental and internal structure with perfect dendrimers is performed using SANS, dynamic light scattering and viscosity analysis, microscopy and molecular dynamics simulation. The interpretation of the results reveals unique structural characteristics arising from lower segmental density of the core, which turns into a soft nano‐sphere with a smooth surface even in the first generation.     

Biocatalytic Feedback‐Driven Temporal Programming of Self‐Regulating Peptide Hydrogels

Switchable self‐assemblies respond to external stimuli with a transition between near‐equilibrium states. Although being a key to present‐day advanced materials, these systems respond rather passively, and do not display autonomous dynamics. For autonomous behavior, approaches must be found to orchestrate the time domain of self‐assemblies, which would lead to new generations of dynamic and self‐regulating materials. Herein, we demonstrate catalytic control of the time domain of pH‐responsive peptide hydrogelators in a closed system. We program transient acidic pH states by combining a fast acidic activator with the slow, enzymatic, feedback‐driven generation of a base (dormant deactivator). This transient state can be programmed over orders of magnitude in time. It is coupled to dipeptides to create autonomously self‐regulating, dynamic gels with programmed lifetimes, which are used for fluidic guidance, burst release, and self‐erasing rapid prototyping.     

The Cage Structure of IndanCHF3 is Based on the Cooperative Effects of CH⋅⋅⋅π and CH⋅⋅⋅F Weak Hydrogen Bonds

The structural and energetic features of the C?H???π interaction and the internal dynamics of the CHF₃ group change drastically in going from benzene?CHF₃ to indan?CHF₃, according to the analysis of the rotational spectrum of the latter complex generated in a supersonic expansion.     

On a Model of a Currency Exchange Rate – Local Stability and Periodic Solutions

A delay differential equation is presented which models how the behavior of traders influences the short time price movements of an asset. Sensitivity to price changes is measured by a parameter a. There is a single equilibrium solution, which is non-hyperbolic for all a>0. We prove that for a< 1 the equilibrium is asymptotically stable, and that for a>1 a 2-dimensional global center-unstable manifold connects the equilibrium to a periodic orbit. Its birth at a=1 is not of Hopf type and seems part of a Takens–Bogdanov scenario.     

Janus cylinders at liquid-liquid interfaces

We describe the first study on the self-assembly behavior of Janus cylinders at liquid/liquid interfaces. The Janus cylinders are characterized by a phase separation along the major axis into two hemicylinders of different wettability. The pendant drop technique and microscopic imaging were used to characterize the adsorption behavior and self-assembly of Janus cylinders at perfluorinated oil/dioxane and perfluorinated oil/dimethyl sulfoxide interfaces. According to the evolution of the interfacial tension and a series of TEM images taken during the cylinder adsorption, we will specify the characteristics of early to late stages of the Janus cylinder adsorption at a liquid-liquid interface and discuss the effect of Janus cylinder length and their concentration. We also establish that the broken symmetry of the corona leads to significantly higher interfacial activity as compared to homogeneous core-shell cylinders. The adsorption is characterized by three different adsorption stages: first, free diffusion to the interface, followed by continuous adsorption of cylinders including ordering and domain formation and, finally, additional packing with a rearrangement of domains and formation of a loose multilayer system.     

Optical coherence tomography in biomedical research

Optical coherence tomography (OCT) is a noninvasive, high-resolution, interferometric imaging modality using near-infrared light to acquire cross-sections and three-dimensional images of the subsurface microstructure of biological specimens. Because of rapid improvement of the acquisition speed and axial resolution of OCT over recent years, OCT is becoming increasingly attractive for applications in biomedical research. Therefore, OCT is no longer used solely for structural investigations of biological samples but also for functional examination, making it potentially useful in bioanalytical science. The combination of in vivo structural and functional findings makes it possible to obtain thorough knowledge on basic physiological and pathological processes. Advanced applications, for example, optical biopsy in visceral cavities, have been enabled by combining OCT with established imaging modalities. This report gives an outline of the state of the art and novel trends of innovative OCT approaches in biomedical research in which the main focus is on applications in fundamental research and pre-clinical utilization.