Talbot quadratures and rational approximations

Many computational problems can be solved with the aid of contour integrals containing $e^z$ in the the integrand: examples include inverse Laplace transforms, special functions, functions of matrices and operators, parabolic PDEs, and reaction-diffusion equations. One approach to the numerical quadrature of such integrals is to apply the trapezoid rule on a Hankel contour defined by a suitable change of variables. Optimal parameters for three classes of such contours have recently been derived: (a) parabolas, (b) hyperbolas, and (c) cotangent contours, following Talbot in 1979. The convergence rates for these optimized quadrature formulas are very fast: roughly $O(3^{-N})$, where $N$ is the number of sample points or function evaluations. On the other hand, convergence at a rate apparently about twice as fast, $O(9.28903^{-N})$, can be achieved by using a different approach: best supremum-norm rational approximants to $e^z$ for $z\in (-\infty,0]$, following Cody, Meinardus and Varga in 1969. (All these rates are doubled in the case of self-adjoint operators or real integrands.) It is shown that the quadrature formulas can be interpreted as rational approximations and the rational approximations as quadrature formulas, and the strengths and weaknesses of the different approaches are discussed in the light of these connections. A MATLAB function is provided for computing Cody--Meinardus--Varga approximants by the method of Carathèodory-Fejèr approximation

Superluminality in the Fierz--Pauli massive gravity

We study the propagation of helicity-1 gravitons in the Fierz--Pauli massive gravity in nearly Minkowski backgrounds. We show that, generically, there exist backgrounds consistent with field equations, in which the propagation is superluminal. The relevant distances are much longer than the ultraviolet cutoff length inherent in the Fierz--Pauli gravity, so superluminality occurs within the domain of validity of the effective low energy theory. There remains a possibility that one may get rid of this property by imposing fine tuning relations between the coefficients in the non-linear generalization of the Fierz--Pauli mass term, order by order in non-linearity; however, these relations are not protected by any obvious symmetry. Thus, among others, superluminality is a problematic property to worry about when attempting to construct infrared modifications of General Relativity.Comment: 11 pages, no figure

Viscoelasticity and metastability limit in supercooled liquids

A supercooled liquid is said to have a kinetic spinodal if a temperature Tsp exists below which the liquid relaxation time exceeds the crystal nucleation time. We revisit classical nucleation theory taking into account the viscoelastic response of the liquid to the formation of crystal nuclei and find that the kinetic spinodal is strongly influenced by elastic effects. We introduce a dimensionless parameter \lambda, which is essentially the ratio between the infinite frequency shear modulus and the enthalpy of fusion of the crystal. In systems where \lambda is larger than a critical value \lambda_c the metastability limit is totally suppressed, independently of the surface tension. On the other hand, if \lambda < \lambda_c a kinetic spinodal is present and the time needed to experimentally observe it scales as exp[\omega/(\lambda_c-\lambda)^2], where \omega is roughly the ratio between surface tension and enthalpy of fusion

Homogeneous bubble nucleation limit of mercury under the normal working conditions of the planned European Spallation Source

In spallation neutron sources, liquid mercury is the subject of big thermal and pressure shocks, upon adsorbing the proton beam. These changes can cause unstable bubbles in the liquid, which can damage the structural material. While there are methods to deal with the pressure shock, the local temperature shock cannot be avoided. In our paper we calculated the work of the critical cluster formation (i.e. for mercury micro-bubbles) together with the rate of their formation (nucleation rate). It is shown that the homogeneous nucleation rates are very low even after adsorbing several proton pulses, therefore the probability of temperature induced homogeneous bubble nucleation is negligible.Comment: 22 Pages, 11 figures, one of them is colour, we plan to publish it in Eur. Phys. J.

Capillary pressure of van der Waals liquid nanodrops

The dependence of the surface tension on a nanodrop radius is important for the new-phase formation process. It is demonstrated that the famous Tolman formula is not unique and the size-dependence of the surface tension can distinct for different systems. The analysis is based on a relationship between the surface tension and disjoining pressure in nanodrops. It is shown that the van der Waals interactions do not affect the new-phase formation thermodynamics since the effect of the disjoining pressure and size-dependent component of the surface tension cancel each other.Comment: The paper is dedicated to the 80th anniversary of A.I. Rusano

Constrained Dynamics of Universally Coupled Massive Spin 2-spin 0 Gravities

The 2-parameter family of massive variants of Einstein's gravity (on a Minkowski background) found by Ogievetsky and Polubarinov by excluding lower spins can also be derived using universal coupling. A Dirac-Bergmann constrained dynamics analysis seems not to have been presented for these theories, the Freund-Maheshwari-Schonberg special case, or any other massive gravity beyond the linear level treated by Marzban, Whiting and van Dam. Here the Dirac-Bergmann apparatus is applied to these theories. A few remarks are made on the question of positive energy. Being bimetric, massive gravities have a causality puzzle, but it appears soluble by the introduction and judicious use of gauge freedom.Comment: 6 pages; Talk given at QG05, Cala Gonone (Italy), September 200

Atomic scale investigation of Cr precipitation in copper

The early stage of the chromium precipitation in copper was analyzed at the atomic scale by Atom Probe Tomography (APT). Quantitative data about the precipitate size, 3D shape, density, composition and volume fraction were obtained in a Cu-1Cr-0.1Zr (wt.%) commercial alloy aged at 713K. Surprisingly, nanoscaled precipitates exhibit various shapes (spherical, plates and ellipsoid) and contain a large amount of Cu (up to 50%), in contradiction with the equilibrium Cu-Cr phase diagram. APT data also show that some impurities (Fe) may segregate along Cu/Cr interfaces. The concomitant evolution of the precipitate shape and composition as a function of the aging time is discussed. A special emphasis is given on the competition between interfacial and elastic energy and on the role of Fe segregation

Association between genetic variants in the Coenzyme Q10 metabolism and Coenzyme Q10 status in humans

<p>Abstract</p> <p>Background</p> <p>Coenzyme Q₁₀(CoQ₁₀) is essential for mitochondrial energy production and serves as an antioxidants in extra mitochondrial membranes. The genetics of primary CoQ₁₀deficiency has been described in several studies, whereas the influence of common genetic variants on CoQ₁₀status is largely unknown. Here we tested for non-synonymous single-nucleotidepolymorphisms (SNP) in genes involved in the biosynthesis (CoQ3^G272S, CoQ6^M406V, CoQ7^M103T), reduction (NQO1^P187S, NQO2^L47F) and metabolism (apoE3/4) of CoQ₁₀and their association with CoQ₁₀status. For this purpose, CoQ₁₀serum levels of 54 healthy male volunteers were determined before (T₀) and after a 14 days supplementation (T₁₄) with 150 mg/d of the reduced form of CoQ₁₀.</p> <p>Findings</p> <p>At T₀, the CoQ₁₀level of heterozygous NQO1^P187Scarriers were significantly lower than homozygous S/S carriers (0.93 ± 0.25 μM versus 1.34 ± 0.42 μM, p = 0.044). For this polymorphism a structure homology-based method (PolyPhen) revealed a possibly damaging effect on NQO1 protein activity. Furthermore, CoQ₁₀plasma levels were significantly increased in apoE4/E4 genotype after supplementation in comparison to apoE2/E3 genotype (5.93 ± 0.151 μM versus 4.38 ± 0.792 μM, p = 0.034). Likewise heterozygous CoQ3^G272Scarriers had higher CoQ₁₀plasma levels at T₁₄compared to G/G carriers but this difference did not reach significance (5.30 ± 0.96 μM versus 4.42 ± 1.67 μM, p = 0.082).</p> <p>Conclusions</p> <p>In conclusion, our pilot study provides evidence that NQO1^P187Sand apoE polymorphisms influence CoQ₁₀status in humans.</p

Asymptotic analysis of the model for distribution of high-tax payers

The z-transform technique is used to investigate the model for distribution of high-tax payers, which is proposed by two of the authors (K. Y and S. M) and others. Our analysis shows an asymptotic power-law of this model with the exponent -5/2 when a total ``mass'' has a certain critical value. Below the critical value, the system exhibits an ordinary critical behavior, and scaling relations hold. Above the threshold, numerical simulations show that a power-law distribution coexists with a huge ``monopolized'' member. It is argued that these behaviors are observed universally in conserved aggregation processes, by analizing an extended model.Comment: 5pages, 3figure