Constructive factorization of LPDO in two variables

We study conditions under which a partial differential operator of arbitrary order $n$ in two variables or ordinary linear differential operator admits a factorization with a first-order factor on the left. The factorization process consists of solving, recursively, systems of linear equations, subject to certain differential compatibility conditions. In the generic case of partial differential operators one does not have to solve a differential equation. In special degenerate cases, such as ordinary differential, the problem is finally reduced to the solution of some Riccati equation(s). The conditions of factorization are given explicitly for second- and, and an outline is given for the higher-order case.Comment: 16 pages, to be published in Journal "Theor. Math. Phys." (2005

Tailoring the frictional properties of granular media

A method of modifying the roughness of soda-lime glass spheres is presented, with the purpose of tuning inter-particle friction. The effect of chemical etching on the surface topography and the bulk frictional properties of grains is systematically investigated. The surface roughness of the grains is measured using white light interferometry and characterised by the lateral and vertical roughness length scales. The underwater angle of repose is measured to characterise the bulk frictional behaviour. We observe that the co-efficient of friction depends on the vertical roughness length scale. We also demonstrate a bulk surface roughness measurement using a carbonated soft drink.Comment: 10 pages, 17 figures, submitted to Phys. Rev.

Mass varying dark matter in effective GCG scenarios

A unified treatment of mass varying dark matter coupled to cosmon-{\em like} dark energy is shown to result in {\em effective} generalized Chaplygin gas (GCG) scenarios. The mass varying mechanism is treated as a cosmon field inherent effect. Coupling dark matter with dark energy allows for reproducing the conditions for the present cosmic acceleration and for recovering the stability resulted from a positive squared speed of sound c_{s}^{\2}, as in the GCG scenario. The scalar field mediates the nontrivial coupling between the dark matter sector and the sector responsible for the accelerated expansion of the universe. The equation of state of perturbations is the same as that of the background cosmology so that all the effective results from the GCG paradigm are maintained. Our results suggest the mass varying mechanism, when obtained from an exactly soluble field theory, as the right responsible for the stability issue and for the cosmic acceleration of the universe.Comment: 17 pages, 3 figure

Interacting dark energy in f(R)f(R) gravity

The field equations in $f(R)$ gravity derived from the Palatini variational principle and formulated in the Einstein conformal frame yield a cosmological term which varies with time. Moreover, they break the conservation of the energy--momentum tensor for matter, generating the interaction between matter and dark energy. Unlike phenomenological models of interacting dark energy, $f(R)$ gravity derives such an interaction from a covariant Lagrangian which is a function of a relativistically invariant quantity (the curvature scalar $R$). We derive the expressions for the quantities describing this interaction in terms of an arbitrary function $f(R)$, and examine how the simplest phenomenological models of a variable cosmological constant are related to $f(R)$ gravity. Particularly, we show that $\Lambda c^2=H^2(1-2q)$ for a flat, homogeneous and isotropic, pressureless universe. For the Lagrangian of form $R-1/R$, which is the simplest way of introducing current cosmic acceleration in $f(R)$ gravity, the predicted matter--dark energy interaction rate changes significantly in time, and its current value is relatively weak (on the order of 1% of $H_0$), in agreement with astronomical observations.Comment: 8 pages; published versio

Two-fluid matter-quintessence FLRW models: energy transfer and the equation of state of the universe

Recent observations support the view that the universe is described by a FLRW model with $\Omega_m^0 \approx 0.3$, $\Omega_{\Lambda}^0 \approx 0.7$, and $w \leq -1/3$ at the present epoch. There are several theoretical suggestions for the cosmological $\Lambda$ component and for the particular form of the energy transfer between this dark energy and matter. This gives a strong motive for a systematic study of general properties of two-fluid FLRW models. We consider a combination of one perfect fluid, which is quintessence with negative pressure ($p_Q = w\epsilon_Q$), and another perfect fluid, which is a mixture of radiation and/or matter components with positive pressure ($p = \beta \epsilon_m$), which define the associated one-fluid model ($p = \gamma \epsilon$). We introduce a useful classification which contains 4 classes of models defined by the presence or absence of energy transfer and by the stationarity ($w = const.$ and $\beta = const.$) or/and non stationarity ($w$ or $\beta$ time dependent) of the equations of state. It is shown that, for given $w$ and $\beta$, the energy transfer defines $\gamma$ and, therefore, the total gravitating mass and dynamics of the model. We study important examples of two-fluid FLRW models within the new classification. The behaviour of the energy content, gravitating mass, pressure, and the energy transfer are given as functions of the scale factor. We point out three characteristic scales, $a_E$, $a_{\cal P}$ and $a_{\cal M}$, which separate periods of time in which quintessence energy, pressure and gravitating mass dominate. Each sequence of the scales defines one of 6 evolution types

Palladium nanoparticles by electrospinning from poly(acrylonitrile-co-acrylic acid)-PdCl2 solutions. Relations between preparation conditions, particle size, and catalytic activity

Catalytic palladium (Pd) nanoparticles on electrospun copolymers of acrylonitrile and acrylic acid (PAN-AA) mats were produced via reduction of PdCl2 with hydrazine. Fiber mats were electrospun from homogeneous solutions of PAN-AA and PdCl2 in dimethylformamide (DMF). Pd cations were reduced to Pd metals when fiber mats were treated in an aqueous hydrazine solution at room temperature. Pd atoms nucleate and form small crystallites whose sizes were estimated from the peak broadening of X-ray diffraction peaks. Two to four crystallites adhere together and form agglomerates. Agglomerate sizes and fiber diameters were determined by scanning and transmission electron microscopy. Spherical Pd nanoparticles were dispersed homogeneously on the electrospun nanofibers. The effects of copolymer composition and amount of PdCl2 on particle size were investigated. Pd particle size mainly depends on the amount of acrylic acid functional groups and PdCl2 concentration in the spinning solution. Increasing acrylic acid concentration on polymer chains leads to larger Pd nanoparticles. In addition, Pd particle size becomes larger with increasing PdCl2 concentration in the spinning solution. Hence, it is possible to tune the number density and the size of metal nanoparticles. The catalytic activity of the Pd nanoparticles in electrospun mats was determined by selective hydrogenation of dehydrolinalool (3,7-dimethyloct-6- ene-1-yne-3-ol, DHL) in toluene at 90 °C. Electrospun fibers with Pd particles have 4.5 times higher catalytic activity than the current Pd/Al2O3 catalyst

Comparing persistence diagrams through complex vectors

The natural pseudo-distance of spaces endowed with filtering functions is precious for shape classification and retrieval; its optimal estimate coming from persistence diagrams is the bottleneck distance, which unfortunately suffers from combinatorial explosion. A possible algebraic representation of persistence diagrams is offered by complex polynomials; since far polynomials represent far persistence diagrams, a fast comparison of the coefficient vectors can reduce the size of the database to be classified by the bottleneck distance. This article explores experimentally three transformations from diagrams to polynomials and three distances between the complex vectors of coefficients.Comment: 11 pages, 4 figures, 2 table

Phantom universe from CPT symmetric QFT

Inspired by the generalization of quantum theory for the case of non-Hermitian Hamiltonians with CPT symmetry, we construct a simple classical cosmological scalar field based model describing a smooth transition from ordinary dark energy to the phantom one

Progressive ataxia with oculo-palatal tremor and optic atrophy

The final publication is available at Springer via doi: 10.​1007/​s00415-013-7136-