Monochromatic surface waves on impermeable boundaries in two-component poroelastic media

The dispersion relation for surface waves on an impermeable boundary of a fully saturated poroelastic medium is investigated numerically over the whole range of applicable frequencies. To this aim a linear simplified model of a two-component poroelastic medium is used. Similarly to the classical Biot’s model, it is a continuum mechanical model but it is much simpler due to the lack of coupling of stresses. However, results for bulk waves following for these two models agree very well indeed which motivates the application of the simplified model in the analysis of surface waves. In the whole range of frequencies there exist two modes of surface waves corresponding to the classical Rayleigh and Stoneley waves. The numerical results for velocities and attenuations of these waves are shown for different values of the bulk permeability coefficient in different ranges of frequencies. In particular, we expose the low and high frequency limits, and demonstrate the existence of the Stoneley wave in the whole range of frequencies as well as the leaky character of the Rayleigh wave.     

Shock waves in polycrystalline iron

The propagation of shock waves through polycrystalline iron is explored by large-scale atomistic simulations. For large enough shock strengths the passage of the wave causes the body-centered-cubic phase to transform into a close-packed phase with most structure being isotropic hexagonal-close-packed (hcp) and, depending on shock strength and grain orientation, some fraction of face-centered-cubic (fcc) structure. The simulated shock Hugoniot is compared to experiments. By calculating the extended x-ray absorption fine structure (EXAFS) directly from the atomic configurations, a comparison to experimental EXAFS measurements of nanosecond-laser shocks shows that the experimental data is consistent with such a phase transformation. However, the atomistically simulated EXAFS spectra also show that an experimental distinction between the hcp or fcc phase is not possible based on the spectra alone.     

Linear Elastic Wave Propagation in Unsaturated Sands,Silts, Loams and Clays

Due to its propitious material properties sandstone is the most studied porous medium for the investigation of linear wave propagation. However, in practical applications the behavior of other soil types, i.e., especially the three main soil types sand, silt, and clay, are much more important. Therefore, the model for partially saturated soils introduced by Albers (Habilitation Thesis, 2010a) is applied to 11 soil types classified in the German standard DIN 4220 to obtain information on the phase velocities and attenuations of the three longitudinal waves and the shear wave appearing in such media.     

Driving oxygen coordinated ligand exchange at nanocrystal surfaces using trialkylsilylated chalcogenides

A general, efficient method is demonstrated for exchanging native oxyanionic ligands on inorganic nanocrystals with functional trimethylsilylated (TMS) chalcogenido ligands. In addition, newly synthesized TMS mixed chalcogenides leverage preferential reactivity of TMS-S bonds over TMS-O bonds, enabling efficient transfer of luminescent nanocrystals into aqueous media with retention of their optical properties.     

Iron(II) template synthesis of benzannulated triphospha- and triarsamacrocycles

Nine-membered 1,4,7-triphospha- and triarsamacrocycles with unsaturated benzo-backbones have been prepared using the [Cp(R)Fe](+) unit as a template. The cyclisation involves the attack of a coordinated phosphide (or arsenide) nucleophile at an activated, electrophilic ortho-fluorophenyl substituent on a neighbouring pnictide donor. The macrocycle assembly is of the 2 + 1 type where two new chelate rings are formed from appropriately derivatised bidentate and monodentate phosphines/arsines. Both [(η(5)-C(5)H(5))Fe](+) and [(η(5)-C(5)Me(5))Fe](+) may be employed for the cyclisation with higher yields generally being observed with the unsubstituted Cp. All new compounds have been characterised by spectroscopic and analytical methods including the single-crystal X-ray structure determination of [(η(5)-C(5)H(5))Fe(tribenzo-9aneP(3)-Ph,Ph(F)(2))](+), 3a, and [(η(5)-C(5)H(5))Fe(tribenzo-9aneAs(3)-Ph,Ph(F)(2))](+), 5, as the tetraphenylborate salts. The crystal structures are isomorphous and show the unique conformation of these new macrocycles with a 'cup shaped' cavity formed by the rigid benzo-backbones. The 9aneAs(3) derivative is the first example of a nine-membered triarsamacrocycle.     

Controlled supramolecular oligomerization of C3-symmetrical molecules in water: the impact of hydrophobic shielding

The supramolecular oligomerization of three water-soluble C(3)-symmetrical discotic molecules is reported. The compounds all possess benzene-1,3,5-tricarboxamide cores and peripheral Gd(III)-DTPA (diethylene triamine pentaacetic acid) moieties, but differ in their linker units and thus in their propensity to undergo secondary interactions in H(2)O. The self-assembly behavior of these molecules was studied in solution using circular dichroism, UV/Vis spectroscopy, nuclear magnetic resonance, and cryogenic transmission electron microscopy. The aggregation concentration of these molecules depends on the number of secondary interactions and on the solvophobic character of the polymerizing moieties. Hydrophobic shielding of the hydrogen-bonding motif in the core of the discotic is of paramount importance for yielding stable, helical aggregates that are designed to be restricted in size through anti-cooperative, electrostatic, repulsive interactions.     

Translated points and Rabinowitz Floer homology

We prove that if a contact manifold admits an exact filling, then every local contactomorphism isotopic to the identity admits a translated point in the interior of its support, in the sense of Sandon [Internat. J. Math. 23 (2012), 1250042]. In addition, we prove that if the Rabinowitz Floer homology of the filling is nonzero, then every contactomorphism isotopic to the identity admits a translated point, and if the Rabinowitz Floer homology of the filling is infinite dimensional, then every contactomorphism isotopic to the identity has either infinitely many translated points, or a translated point on a closed leaf. Moreover, if the contact manifold has dimension greater than or equal to 3, the latter option generically does not happen. Finally, we prove that a generic compactly supported contactomorphism on ${\mathbb{R}^{2n+1}}$ has infinitely many geometrically distinct iterated translated points all of which lie in the interior of its support.     

Exponential decay for sc-gradient flow lines

In this paper we introduce the notion of sc-action functionals and their sc-gradient flow lines. Our approach is inspired by Floer’s unregularized gradient flow. The main result of this paper is that under a Morse condition, sc-gradient flow lines have uniform exponential decay towards critical points. The ultimate goal for the future is to construct an M-polyfold bundle over an M-polyfold such that the space of broken sc-gradient flow lines is the zero set of an appropriate sc-section. Here uniform exponential decay is essential. Of independent interest is that we derive exponential decay estimates using interpolation inequalities as opposed to Sobolev inequalities. An advantage is that interpolation inequalities are independent of the dimension of the source space.     

Comparison of different mathematical models of diffusion-weighted prostate MR imaging

Purpose

To evaluate which mathematical model (monoexponential, biexponential, statistical, kurtosis) fits best to the diffusion-weighted signal in prostate magnetic resonance imaging (MRI).

Materials and Methods

24 prostate 3-T MRI examinations of young volunteers (YV, n= 8), patients with biopsy proven prostate cancer (PC, n= 8) and an aged matched control group (AC, n= 8) were included. Diffusion-weighted imaging was performed using 11 b-values ranging from 0 to 800 s/mm².

Results

Monoexponential apparent diffusion coefficient (ADC) values were significantly (P<.001) lower in the peripheral (PZ) zone (1.18±0.16 mm²/s) and the central (CZ) zone (0.73±0.13 mm²/s) of YV compared to AC (PZ 1.92±0.17 mm²/s; CZ 1.35±0.21 mm²/s). In PC ADC_mono values (0.61±0.06 mm²/s) were significantly (P<.001) lower than in the peripheral of central zone of AC. Using the statistical analysis (Akaike information criteria) in YV most pixels were best described by the biexponential model (82%), the statistical model, respectively kurtosis (93%) each compared to the monoexponential model. In PC the majority of pixels was best described by the monoexponential model (57%) compared to the biexponential model.

Conclusion

Although a more complex model might provide a better fitting when multiple b-values are used, the monoexponential analyses for ADC calculation in prostate MRI is sufficient to discriminate prostate cancer from normal tissue using b-values ranging from 0 to 800 s/mm².