Design of Anisotropic Diffusion Hardware Fiber Phantoms

A gold standard for the validation of diffusion weighted magnetic resonance imaging (DW-MRI) in brain white matter (WM) is essential for clinical purposes but still not available. Synthetic anisotropic fiber bundles are proposed as phantoms for the validation of DW-MRI because of their well-known structure, their long preservability and the possibility to create complex geometries such as curved and fiber crossings. A crucial question is how the different material properties and size of the fiber phantoms influence the outcome of the DW-MRI experiment. Several fiber materials are compared in this study. The effect of surface relaxation and internal gradients on the SNR is evaluated. In addition, the dependency of the fiber density and fiber radius on the diffusion properties is investigated

Driven polymer translocation through a nanopore: a manifestation of anomalous diffusion

We study the translocation dynamics of a polymer chain threaded through a nanopore by an external force. By means of diverse methods (scaling arguments, fractional calculus and Monte Carlo simulation) we show that the relevant dynamic variable, the translocated number of segments $s(t)$, displays an {\em anomalous} diffusive behavior even in the {\em presence} of an external force. The anomalous dynamics of the translocation process is governed by the same universal exponent $\alpha = 2/(2\nu +2 - \gamma_1)$, where $\nu$ is the Flory exponent and $\gamma_1$ - the surface exponent, which was established recently for the case of non-driven polymer chain threading through a nanopore. A closed analytic expression for the probability distribution function $W(s, t)$, which follows from the relevant {\em fractional} Fokker - Planck equation, is derived in terms of the polymer chain length $N$ and the applied drag force $f$. It is found that the average translocation time scales as $\tau \propto f^{-1}N^{\frac{2}{\alpha} -1}$. Also the corresponding time dependent statistical moments, $\propto t^{\alpha}$ and $\propto t^{2\alpha}$ reveal unambiguously the anomalous nature of the translocation dynamics and permit direct measurement of $\alpha$ in experiments. These findings are tested and found to be in perfect agreement with extensive Monte Carlo (MC) simulations.Comment: 6 pages, 4 figures, accepted to Europhys. Lett; some references were supplemented; typos were correcte

Dielectric tensor of monoclinic Ga2_2O3_3 single crystals in the spectral range 0.5−8.5 0.5 - 8.5\,eV

The dielectric tensor of $\beta$-Ga$_2$O$_3$ was determined by generalized spectroscopic ellipsometry in a wide spectral range from $0.5\,\mathrm{eV}$ to $8.5\,\mathrm{eV}$ as well as by calculation including quasiparticle bands and excitonic effects. The dielectric tensors obtained by both methods are in excellent agreement with each other and the observed transitions in the dielectric function are assigned to the corresponding valence bands. It is shown that the off-diagonal element of the dielectric tensor reaches values up to $|\varepsilon_{xz} | \approx 0.30$ and cannot be neglected. Even in the transparent spectral range where it is quite small ($|\varepsilon_{xz} | < 0.02$) it causes a rotation of the dielectric axes around the symmetry axis of up to $20^\circ$

A two-species continuum model for aeolian sand transport

Starting from the physics on the grain scale, we develop a simple continuum description of aeolian sand transport. Beyond popular mean-field models, but without sacrificing their computational efficiency, it accounts for both dominant grain populations, hopping (or "saltating") and creeping (or "reptating") grains. The predicted stationary sand transport rate is in excellent agreement with wind tunnel experiments simulating wind conditions ranging from the onset of saltation to storms. Our closed set of equations thus provides an analytically tractable, numerically precise, and computationally efficient starting point for applications addressing a wealth of phenomena from dune formation to dust emission.Comment: 23 pages, 9 figure

Grassmann Variables and Pseudoclassical Nuclear Magnetic Resonance

The concept of a propagator is useful and is a well-known object in diffusion NMR experiments. Here, we investigate the related concept; the propagator for the magnetisation or the Green's function of the Torrey-Bloch equations. The magnetisation propagator is constructed by defining functions such as the Hamiltonian and Lagrangian and using these to define a path integral. It is shown that the equations of motion derived from the Lagrangian produce complex-valued trajectories (classical paths) and it is conjectured that the end-points of these trajectories are real-valued. The complex nature of the trajectories also suggests that the spin degrees of freedom are also encoded into the trajectories and this idea is explored by explicitly modeling the spin or precessing magnetisation by anticommuting Grassmann variables. A pseudoclassical Lagrangian is constructed by combining the diffusive (bosonic) Lagrangian with the Grassmann (fermionic) Lagrangian, and performing the path integral over the Grassmann variables recovers the original Lagrangian that was used in the construction of the propagator for the magnetisation. The trajectories of the pseudoclassical model also provide some insight into the nature of the end-points.Comment: 25 page

Nonequilibrium field-induced phase separation in single-file diffusion

Using an analytically tractable lattice model for reaction-diffusion processes of hard-core particles we demonstrate that under nonequilibrium conditions phase coexistence may arise even if the system is effectively one-dimensional as e.g. in the channel system of some zeolites or in artificial optical lattices. In our model involving two species of particles a steady-state particle current is maintained by a density gradient between the channel boundaries and by the influence of an external driving force. This leads to the development of a fluctuating but always microscopically sharp interface between two domains of different densities which are fixed by the boundary chemical potentials. The internal structure of the interface becomes very simple for strong driving force. We calculate the drift velocity and diffusion coefficient of the interface in terms of the microscopic model parameters.Comment: 38 pages, 2 figure

Autocatalytic reaction-diffusion processes in restricted geometries

We study the dynamics of a system made up of particles of two different species undergoing irreversible quadratic autocatalytic reactions: $A + B \to 2A$. We especially focus on the reaction velocity and on the average time at which the system achieves its inert state. By means of both analytical and numerical methods, we are also able to highlight the role of topology in the temporal evolution of the system

Magnetic Resonance Imaging of Gas Hydrate Formation and Conversion at Sub-Seafloor Conditions

The production of natural gas from sub-seafloor gas hydrates is one possible strategy to meet the world’s growing demand for energy. On the other hand, climate warming scenarios call for the substitution of fossil energy resources by sustainable energy concepts. Burning natural gas from gas hydrates could be emission neutral if it was combined with a safe storage of the emitted CO2. Laboratory experiments, that address corresponding strategies, need to be performed under high pressures and low temperatures to meet the thermodynamic conditions of the sub-seafloor environment. In this paper, we present a high-pressure flow-through sample cell that is suitable for nuclear magnetic resonance (NMR) experiments at realistic marine environmental conditions, i.e. pressures up to 15 MPa and temperatures from 5 to 20 °C, and we demonstrate its suitability in applied gas hydrate research

Identification of a possible superconducting transition above room temperature in natural graphite crystals

Measuring with high precision the electrical resistance of highly ordered natural graphite samples from a Brazil mine, we have identified a transition at $\sim$350~K with $\sim$40~K transition width. The step-like change in temperature of the resistance, its magnetic irreversibility and time dependence after a field change, consistent with trapped flux and flux creep, and the partial magnetic flux expulsion obtained by magnetization measurements, suggest the existence of granular superconductivity below 350~K. The zero-field virgin state can only be reached again after zero field cooling the sample from above the transition. Paradoxically, the extraordinarily high transition temperature we found for this and several other graphite samples is the reason why this transition remained undetected so far. The existence of well ordered rhombohedral graphite phase in all measured samples has been proved by x-rays diffraction measurements, suggesting its interfaces with the Bernal phase as a possible origin for the high-temperature superconductivity, as theoretical studies predicted. The localization of granular superconductivity at these two dimensional interfaces prevents the observation of a zero resistance state or of a full Meissner state.Comment: 14 pages with 21 figure

The effects of halogen elements on the opening of an icosahedral B12 framework

The fully halogenated or hydrogenated B12X12 (X = H, F, Cl, Br and I) clusters are confirmed to be icosahedral. On the other hand, the bare B12 cluster is shown to have a planar structure. A previous study showed that a transformation from an icosahedron to a plane happens when 5 to 7 iodine atoms are substituted. Later, the transition was confirmed to be seven iodine substitutions based on an infrared spectroscopy study. In this study, we investigated the effects of different halogen atoms on the opening of the B12 icosahedral cage by means of density functional theory calculations. We found that the halogen elements do not have significant effects on the geometries of the clusters. The computed IR spectra show similar representative peaks for all halogen substituted clusters. Interestingly, we found a blue-shift in the IR spectra with the increase in the mass of the halogen atoms. Further, we compared the Gibbs free energies at different temperatures for different halogen atoms. The results show that the Gibbs free energy differences between open and close structures of B12X7 become larger when heavier halogen atoms are present. This interesting finding was subsequently investigated by energy decomposition analysis