Turing invariant sets and the perfect set property

We show that $\text{◂...▸}\mathsf{ZF}+\mathsf{DC}+\text{“all}\text{Turing}\text{invariant}\text{sets}\text{of}\text{reals}\text{have}\text{the}\text{perfect}\text{set}\text{property”}$ implies that all sets of reals have the perfect set property. We also show that this result generalizes to all countable analytic equivalence relations.     

Premicellar aggregation of amphiphilic molecules

We revisit the problem of amphiphilic aggregation using a simple two-state (monomer-aggregate) thermodynamic model, which allows the study of metastable aggregates of variable size. A sequence of well separated concentrations emerge: c(1), where a metastable aggregated state appears; c(2), above which an appreciable amount of metastable aggregates forms; and c(3), where the aggregated state becomes stable. Of these, c(3) is shown to correspond to the critical micelle concentration (cmc) as commonly measured in macroscopic experiments. Thus, appreciable premicellar aggregation is predicted in the concentration range between c(2) and c(3). We show that, so long as the micelles are not too large, the extent of premicellar aggregation is much larger than that expected from mere finite-size effects. It stems from the variability of the micelle size and the small free energy difference between the metastable state, containing monomers and aggregates, and the pure monomeric one. The aggregate size is found to weakly change with concentration below and above the cmc. The existence of premicellar aggregates and their concentration-insensitive size are in agreement with a recent experiment.     

Electron transfer,equilibrium, and protonation in the system of cis- and trans-stilbene in 2-propanol

Spectrophotometric pulse radiolysis experiments with cis- and trans-stilbene (S_c and S_t) in 2-propanol show that both isomers react with the solvated electron with a rate constant of 4.5 × 10⁹ M^?1 s^?1. The absorption spectra of the two anion radicals have maxima at 496 and 486 nm, respectively. The absorbances at 400–550 nm disappear exponentially corresponding to a pseudo first order protonation of the anion radicals. The rate constants for the protonation of the cis isomer is 6.4 × 10⁵ and of the trans isomer 0.7 × 10⁵ s^?1. In mixtures of cis- and trans-stilbene the electron transfer

has a forward rate constant of 9 × 10⁷ M^?1 s^?1 while the back reaction has a rate constant of 2.15 × 10⁷ M^?1 s^?1. An equilibrium constant K = 4.2 is calculated.     

Towards the detection of single polychlorotriphenylmethyl radical derivatives by means of Electron Spin Noise STM

The Electron Spin Noise Scanning Tunnelling Microscopy (ESN-STM) technique is one of the most promising techniques detecting one single spin, combining the spatial resolution of the STM with the ability of spectral resolution and spin manipulation of Electron Spin Resonance. After its first observation, the effectiveness of this technique has been tested by different groups to study the properties of small aggregates or single organic radical molecules.We report on the ongoing ESN-STM study on nano-aggregates of tris(2,4,6-thrichlorophenyl)methyl radical (TTM) derivatives, whose possibility to be used as wires, switches and memory devices has already been investigated in bulk. After deposition on Au(111), TTM radicals preserved their magnetism. To treat the collected noise data we followed a statistical approach; some peculiar characteristics of this analysis will be addressed.     

Rapid MR imaging by sensitivity profile indexing and deconvolution reconstruction (SPID)

A new parallel MR imaging technique, which uses localized information from the elements of a multi-coil array to accelerate imaging, is described. The technique offers an alternative reconstruction approach to currently available techniques (e.g., SMASH and SENSE). Following a partial k-space data acquisition, image reconstruction in this approach proceeds in two steps: first, fitting the measured coil sensitivities to a set of partially localized target functions, a blurred intermediate image of the studied object is produced. Blurring is obtained in a systematic manner, forming images of the studied object convolved with a known convolution kernel. Full spatial resolution is then recovered by deconvolution of the blurred images with the known kernel function. The technique offers flexibility in the arrangement of the acquired signal data k-lines, and a mechanism for controlling reconstruction quality through the convolution the deconvolution procedure. The technique was validated in phantom and in vivo imaging experiments demonstrating high time reduction factors.     

Accelerating CFD–DEM simulation of processes with wide particle size distributions

Size-reduction systems have been extensively used in industry for many years. Nevertheless, reliable engineering tools to be used to predict the comminution of particles are scarce. Computational fluid dynamics(CFD)–discrete element model(DEM) numerical simulation may be used to predict such a complex phenomenon and therefore establish a proper design and optimization model for comminution systems.They may also be used to predict attrition in systems where particle attrition is significant. Therefore,empirical comminution functions(which are applicable for any attrition/comminution process), such as:strength distribution, selection, equivalence, breakage, and fatigue, have been integrated into the threedimensional CFD–DEM simulation tool. The main drawback of such a design tool is the long computational time required owing to the large number of particles and the minute time-step required to maintain a steady solution while simulating the flow of particulate materials with very fine particles.The present study developed several methods to accelerate CFD–DEM simulations: reducing the number of operations carried out at the single-particle level, constructing a DEM grid detached from the CFD grid enabling a no binary search, generating a sub-grid within the DEM grid to enable a no binary search for fine particles, and increasing the computational time-step and eliminating the finest particles in the simulation while still tracking their contribution to the process.The total speedup of the simulation process without the elimination of the finest particles was a factor of about 17. The elimination of the finest particles gave additional speedup of a factor of at least 18.Therefore, the simulation of a grinding process can run at least 300 times faster than the conventional method in which a standard no binary search is employed and the smallest particles are tracked.     

Segregation in reaction-diffusion systems

Segregation of reactants in reaction-diffusion systems is a spatial structure that can be formed either as a result of a dynamical process or as an initially prepared system. In this paper we review our recent results on both such systems. First we study the dynamic segregation at a single trap, in particular in the presence of fields and disorder. Then we study properties of the dynamic reaction front produced due to initial segregation of the reactants in the A + B→C system. Both systems are shown to exhibit anomalous kinetic properties.