Rheological modeling of pasta dough flow processes in channels of convergent-divergent inserts of molding matrix

One of efficient directions for pasta press designs modernization is installation of special conical-and-cylindrical inserts in the matrix wells in front of the dies having, like Venturi tubes, narrowing zones (convergent), expansion (divergent) and a cylindrical path located between them. However, rheological aspects of such method of forming tool modernizing in relation to pasta presses have not been studied, recommendations for structural elements calculation and design have not been developed. All this is a significant obstacle for using the method in engineering and industrial practice. The research purpose is to develop rheological models the pasta dough flow in the conical-cylindrical channels of convergent-divergent inserts and to evaluate with their help the impact of structural dimensions and rheological properties on resistance to pasta dough flow. Pasta dough was considered as a rheological complex nonlinearly viscous plastic material. In technical calculations contribution of shear strength was neglected and a rheological analysis was performed using the Oswald-de-Vila power law equation. Analytical dependences obtained make it possible to calculate the pressure drops in the convergent-divergent insert and its elements. Numerical modeling was performed and calculated data were obtained regarding the impact of dimensions of structural elements of the insert and rheological parameters of pasta dough on its resistance to viscous flow. The results obtained can form the basis of engineering and technological calculations in design of convergent-divergent inserts for laboratory and industrial matrices of pasta presses.

The case for duality violations in the analysis of hadronic τ decays

In this review, we discuss why, in the determination of [Formula: see text] from hadronic [Formula: see text] decays, two important assumptions made in most of previous analyses, namely the neglect of higher-dimension condensates and of duality violations (DVs), have introduced uncontrolled systematic errors into this determination. Although the use of pinched weights is usually offered as a justification of these assumptions, we explain why it is not possible to simultaneously suppress these two contributions; particularly since the Operator Product Expansion (OPE) is expected to be an asymptotic, rather than a convergent expansion. There is not only experimental and theoretical evidence for DVs but they also affect the extraction of [Formula: see text].

An All-Orders Derivative Expansion

We evaluate the exact QED2+1 effective action for fermions in the presence of a family of static but spatially inhomogeneous magnetic field profiles. This exact result yields an all-orders derivative expansion of the effective action, and indicates that the derivative expansion is an asymptotic, rather than a convergent, expansion.

An asymptotic representation for the Riemann zeta function on the critical line

A representation for the Riemann zeta function ζ( s ) is given as an absolutely convergent expansion involving incomplete gamma functions which is valid for all finite complex values of s (≠ 1). It is then shown how use of the uniform asymptotics of the incomplete gamma function leads to a new asymptotic representation for ζ( s ) on the critical line s = ½ + i t when t → ∞. This new result involves an error function smoothing of an infinite sum and consequently shares some similarity to, though is quite different from, the recent asymptotic expansion for ζ(½ + i t ) developed by Berry & Keating. Numerical examples suggest that term for term (with a little extra computational effort) the new representation is at least as accurate as the Riemann–Siegel formula.

Electronic states in complicated materials: the recursion method

The determination of electronic states in complicated materials is difficult because of large numbers of inequivalent and nearly degenerate electronic orbitals. The only available approach is direct integration of the Schrödinger equation by path summation for which the recursion method gives a convergent expansion of the energy resolvent as a continued fraction whose parameters may be expressed as summations of groups of mutually avoiding paths. The inverse Fourier transforms of these continued fractions are matrix elements of the propagator and hence provide convergent discrete approximants for Feynman path integrals. Path counting for sequences of close packed layers is illustrated, and the application of the recursion method to the structural stability of transition metal Laves phases is reviewed briefly.