Helically coiled pipes are widely used in many industrial and engineering applications because of their compactness, larger heat transfer area per unit volume and higher efficiency in heat and mass transfer compared to other pipe geometries. They are commonly encountered in heat exchangers, steam generators in power plants and chemical reactors. The most notable feature of flow in helical pipes is the secondary flow (i.e., the cross-sectional circulatory motion) caused by centrifugal forces due to the curvature. Other important features are the stabilization effects of turbulent flow and the higher Reynolds number at which the transition from a laminar to a turbulent state occurs compared to straight pipes. A survey of the open literature on helical pipe flows shows that a good deal of experimental and theoretical work has been conducted to derive appropriate correlations to predict frictional pressure losses under laminar and turbulent conditions as well as to study the dependence of the flow characteristics and heat transfer capabilities on the Reynolds number, the Nusselt number and the geometrical parameters of the helical pipe. Despite the progress made so far in understanding the flow and heat transfer characteristics of helical pipe flow, there is still much work to be completed to address the more complex problem of multiphase flows and the impact of pipe deformation and corrugation on single- and multiphase flow. The aim of this paper is to provide a review on the state-of-the-art experimental and theoretical research concerning the flow in helically coiled pipes.

We show that a physical correspondence between Brownian motion and quantum mechanics can be established by formal analytic continuation if Wick rotation ($t\to it$) is replaced by the mirror symmetric, complex conjugate time transformation $t\to \pm it$. Invariance of the square modulus of the wave function under this transformation reveals a tight connection between Born's interpretation of the probability density and the proper time $t^2=(-it)(+it)$, as being both the result of a time symmetry breaking in the informational content of the microscopic (quantum) world, which takes place as we move to a macroscopic level. We find that under the transformation $t\to \pm it$, the Schrödinger equation and its complex conjugate conforms with a stochastic-mechanical model of the Brownian motion of a particle. From the present analysis, Nelson's osmotic velocity arises naturally and the quantum phase function admits a classical interpretation in terms of a continuous (scalar) potential field that influences the motion of the particle. The maximum phase variation defines the direction of the osmotic and current velocity. Whereas the paper focuses on the correlation between quantum mechanics and Ficks's second law for a constant diffusion coefficient, a discussion is also provided on the possibility of a quantum mechanical formulation for anomalous diffusion, where the diffusion coefficient is a function of space and/or time.

The local consistency of the method of Smoothed Particle Hydrodynamics (SPH) is proved for a multidimensional continuous mechanical system in the context of measure theory. The Wasserstein distance of the corresponding measure-valued evolutions is used to show that full convergence is achieved in the joint limit N → ∞ and h → 0, where N is the total number of particles that discretize the computational domain and h is the smoothing length. Using an initial local discrete measure given by μ0N=∑b=1Nm(xb,h)δ0,xb(0), where m_b = m(x_b, h) is the mass of particle with label b at position x_b(t) and δ0,x_b(t) is the x_b(t)-centered Dirac delta distribution, full consistency of the SPH method is demonstrated in the above joint limit if the additional limit N → ∞ is also ensured, where N is the number of neighbors per particle within the compact support of the interpolating kernel.

We provide evidence of an extreme form of sensitivity to initial conditions in a family of one-dimensional self-ruling dynamical systems. We prove that some hyperchaotic sequences are closed-form expressions of the orbits of these pseudo-random dynamical systems. Each chaotic system in this family exhibits a sensitivity to initial conditions that encompasses the sequence of choices of the evolution rule in some collection of maps. This opens a possibility to extend current theories of complex behaviors on the basis of intrinsic uncertainty in deterministic chaos.Comment: 18 pages, 13 figure

Los números metálicos son números irracionales en cuanto sus expresiones decimales están conformadas por cifras infinitas que se siguen sin repetir un patrón fijo. El número metálico más celebrado es el llamado número de oro o razón áurea, el cual se encuentra frecuentemente en la naturaleza y que, además, aparece muchas veces en diferentes áreas, incluyendo las matemáticas, la geometría, la física, la arquitectura, el arte, entre otras. Sin embargo, junto al número de oro existe toda una familia de otros números metálicos menos conocidos, como la razón de plata, de bronce, etcétera, que, al igual que la razón áurea, pueden construirse como la razón entre los lados de un segmento o de un rectángulo.