The hydrogen atom as a projection of an homogeneous space

The Kustaanheimo-Stiefel transformation as applied to the nonrelativistic hydrogen atom provides one of the rare examples of a free particle moving on a four-dimensional homogeneous space.     

Stationary phase-based two-dimensional chromatography combining both covalent and noncovalent interactions on a single HPLC column

A new type of 2-D separation material was synthesized and studied. The material is suitable for 2-D chromatography utilizing both covalent and noncovalent interactions. The first dimension is boronate affinity chromatography, and the second dimension is RP chromatography (or vice versa). The polymeric media were prepared using p-vinylphenylboronic acid as the functional monomer. This monomer was selected due to the presence of the boronic acid group for the cis-diol/boronate interaction in boronate chromatography. Two crosslinkers were evaluated, namely ethylene glycol dimethacrylate and divinylbenzene. The crosslinker content was varied to maximize the polymer strength and the RP performance of the packed column. Several parameters were evaluated to define the optimum for polymer strength and column performance including crosslinker, porogen, initiator, and column-packing parameters. The polymer-based HPLC columns were successful in separating phenol, catechol, dimethylphthalate, and hydroquinone under RP conditions, and thus can be used as an RP HPLC column. The columns were also successful in separating catechol and adenosine under boronate chromatography conditions, and thus can be used as a boronate affinity column. Moreover, the two types of chromatography can be performed consecutively on the same column during one complete chromatographic run, making it a 2-D chromatography. Under these 2-D conditions, the catechol was separated from a mixture of phenol, catechol, dimethylphthalate, and hydroquinone; the adenosine ribonucleoside was separated from a mixture of adenosine ribonucleoside, adenosine deoxyribonucleoside, and uridine deoxyribonucleoside. This type of single-column 2-D HPLC eliminates the requirement of a complex and expensive multidimensional HPLC instrument and provides increased peak capacity for separation.     

Softening induced instability of a stretched cohesive granular layer

We report on a cellular pattern which spontaneously forms at the surface of a thin layer of a cohesive granular material submitted to in-plane stretching. We present a simple model in which the mechanism responsible of the instability is the "strain softening" exhibited by humid granular materials above a typical strain. Our analysis indicates that such a type of instability should be observed in any system presenting a negative stress sensitivity to strain perturbations.     

A simple osmotic stress test to predict boar sperm cryosurvival

This work was carried out to test whether viability of pig spermatozoa subjected to an osmotic test is correlated to sperm cryosurvival. Spermatozoa were cooled from 22 degrees C to -5 degrees C, aliquots were exposed to a series of hyperosmotic solutions (300-2100 mOsm/kg) for 15 min, immediately spermatozoa were re-warmed to 37 degrees C and isosmolarity was restored. Spermatozoa were cooled from 22 degrees C to -5 degrees C and one aliquot was exposed to the osmotic test while diluted spermatozoa were frozen-thawed. Plasma membrane-intact spermatozoa decreased as osmolarity increased (P < 0.0001), a further decreased (P < 0.0001) was observed when isotonicity was restored. Proportions of plasma membrane-intact and acrosome-intact cells from the osmotic test were no different from those after freeze-thawing: 36% vs. 35%, 80% vs. 80%, respectively. A significant correlation was found between the proportion of acrosome-intact cells after freeze-thawing and that from the osmotic test (r = 0.81, P <0.01). This test provides a useful and economical mean to predict in vitro boar sperm cryosurvival.     

Biotic patterns in LIGO recordings point to the creativity of gravitational interactions

The waves recorded by the Laser Interferometer Gravitational‐Wave Observatory (LIGO) presumably represent gravitational waves. Time series analyses revealed chaotic characteristics (nonperiodic oscillations, causal generation) and features of creativity that characterize Bios: increasing diversity (as contrasted to convergence to an attractor); novelty (lesser recurrence than randomized copies); and temporal complexity (a succession of different time‐limited patterns). Bios is also observed in quantum, cosmological, biological, and economic processes. Bios can be generated mathematically by bipolar feedback. Finding features of creativity in gravitational waves indicates that gravitational interactions causally generate complex patterns. As the gravitational wave background dates from the trillionth‐of‐a‐second after the Big Bang, these results indicate that causal and creative processes were important in the early universe, in contrast to the presumed predominance of random oscillations. © 2009 Wiley Periodicals, Inc. Complexity, 2010     

Modular forms and effective Diophantine approximation

After the work of G. Frey, it is known that an appropriate bound for the Faltings height of elliptic curves in terms of the conductor (Frey?s height conjecture) would give a version of the ABC conjecture. In this paper we prove a partial result towards Frey?s height conjecture which applies to all elliptic curves over $\mathbb{Q}$, not only Frey curves. Our bound is completely effective and the technique is based in the theory of modular forms. As a consequence, we prove effective explicit bounds towards the ABC conjecture of similar strength to what can be obtained by linear forms in logarithms, without using the latter technique. The main application is a new effective proof of the finiteness of solutions to the S-unit equation (that is, S-integral points of ${\mathbb{P}}^1?\{0,1,\infty \}$), with a completely explicit and effective bound, without using any variant of Baker?s theory or the Thue–Bombieri method.     

Classical spin dynamics of anisotropic Heisenberg dimmers

In the present work we study the deterministic spin dynamics of two interacting anisotropic magnetic particles in the presence of an external magnetic field using the Landau-Lifshitz equation. The interaction between particles is through the exchange energy. We study both conservative and dissipative cases. In the first one, we characterize the dynamical behavior of the system by monitoring the Lyapunov exponents and bifurcation diagrams. In particular, we explore the dependence of the largest Lyapunov exponent respect to the magnitude of applied magnetic field and exchange constant. We find that the system presents multiple transitions between regular and chaotic behaviors. We show that the dynamical phases display a very complicated topology of intricately intermingled chaotic and regular regions. In the dissipative case, we calculate the final saturation states as a function of the magnitude of the applied magnetic field, exchange constant as well as the anisotropy constants.     

An [FeIII34] Molecular Metal Oxide

The dissolution of anhydrous iron bromide in a mixture of pyridine and acetonitrile, in the presence of an organic amine, results in the formation of an [Fe₃₄] metal oxide molecule, structurally characterised by alternate layers of tetrahedral and octahedral Fe^III ions connected by oxide and hydroxide ions. The outer shell of the complex is capped by a combination of pyridine molecules and bromide ions. Magnetic data, measured at temperatures as low as 0.4 K and fields up to 35 T, reveal competing antiferromagnetic exchange interactions; DFT calculations showing that the magnitudes of the coupling constants are highly dependent on both the Fe‐O‐Fe angles and Fe?O distances. The simplicity of the synthetic methodology, and the structural similarity between [Fe₃₄], bulk iron oxides, previous Fe^III–oxo cages, and polyoxometalates (POMs), hints that much larger molecular Fe^III oxides can be made.     

Improved Eddy-Viscosity Modelling of Turbulent Flow around Porous–Fluid Interface Regions

Transport in Porous Media - The RANS modelling of turbulence across fluid-porous interface regions within ribbed channels has been investigated by applying double (both volume and Reynolds)...