SUMMARYA weighted residual collocation methodology for simulating two‐dimensional shear‐driven and natural convection flows has been presented. Using a dyadic mesh refinement, the methodology generates a basis and a multiresolution scheme to approximate a fluid flow. To extend the benefits of the dyadic mesh refinement approach to the field of computational fluid dynamics, this article has studied an iterative interpolation scheme for the construction and differentiation of a basis function in a two‐dimensional mesh that is a finite collection of rectangular elements. We have verified that, on a given mesh, the discretization error is controlled by the order of the basis function. The potential of this novel technique has been demonstrated with some representative examples of the Poisson equation. We have also verified the technique with a dynamical core of a two‐dimensional flow in primitive variables. An excellent result has been observed—on resolving a shear layer and on the conservation of the potential and the kinetic energies—with respect to previously reported benchmark simulations. In particular, the shear‐driven simulation at CFL = 2.5 (Courant–Friedrichs–Lewy) and scriptRe MathClass-rel= 1000 (Reynolds number) exhibits a linear speed up of CPU time with an increase of the time step, Δt. For the natural convection flow, the conversion of the potential energy to the kinetic energy and the conservation of total energy is resolved by the proposed method. The computed streamlines and the velocity fields have been demonstrated. Copyright © 2014 John Wiley & Sons, Ltd.

The Coulomb barrier is a classic introductory physics concept and one that is key to understanding nuclear fusion. Yet the idea that fusing atoms could exhibit both far-range repulsion and short-range attraction can result in significant cognitive dissonance in students. There are no classical examples of this behavior and no commercially available demonstration kits. The magnetic potential energy barrier apparatus allows a visual and tactile demonstration of repulsion at a distance and strong short-range attraction. Students directly experience the role of kinetic energy in overcoming a potential energy barrier.

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Summary The fundamental interaction between tropical cyclones was investigated through a series of water tank experiements by Fujiwhara . However, a complete understanding of tropical cyclones remains an open research challenge although there have been numerous investigations through measurments with aircrafts/satellites, as well as with numerical simulations. This article presents a computational model for simulating the interaction between cyclones. The proposed numerical method is presented briefly, where the time integration is performed by projecting the discrete system onto a Krylov subspace. The method filters the large scale fluid dynamics using a multiresolution approximation, and the unresolved dynamics are modeled with a Smagorinsky type subgrid scale parameterization scheme. Numerical experiments with Fujiwhara interactions are considered to verify modeling accuracy. An excellent agreement between the present simulation and a reference simulation at scriptRe=50.3em000 has been demonstrated. At scriptRe=370.3em440, the kinetic energy of cyclones is seen consolidated into larger scales with concurrent enstrophy cascade – suggesting a steady increase of energy containing scales – a phenomena that is typical in two‐dimensional turbulence theory. The primary results of this article suggest a novel avenue for addressing some of the computational challenges of mesoscale atmospheric circulations. Copyright © 2015 John Wiley & Sons, Ltd.

The Coulomb barrier occurs at the quantum interface between the strong and the electromagnetic fundamental forces. Overcoming the Coulomb barrier is the central goal of nuclear fusion, and an effective model of the barrier can only accelerate the achievement of this potential source of clean and abundant energy. A recently introduced magnetic “Coulomb” barrier model provides a visual and tactile representation of the fusion potential curve, including the counterintuitive combination of far-range repulsion and close-range attraction (https://youtu.be/FzEHs47nylA). The model contains a pair of opposing circular magnet arrays, each array comprising a series of double north-oriented magnets alternating in regular sequence with single south-oriented magnets. This configuration generates complex magnetic fields between the arrays, with the result that the net force between them (attractive or repulsive) depends on the degree of separation. The close-range dynamic simulates the behavior of the strong nuclear force within the Coulomb barrier, and the plot of magnetic force versus distance reproduces the familiar fusion potential curve. Given Maxwell’s unification of electricity and magnetism within the electromagnetic fundamental force, the question arises as to whether alternating and unequal electric fields might also demonstrate a potential barrier. In this exercise, the circular alternating and unequal magnet sequences of each magnet array are replaced by theoretical alternating +1 and -2 coulomb electrostatic charges to produce a pair of opposing electrostatic arrays. The centimeter scale and essential geometry are preserved. Coulomb’s law is then used to calculate component forces at incremental distances between the arrays. The theoretical electrostatic analog of the magnetic "Coulomb" barrier apparatus generates a force/distance curve that is nearly identical to the magnetic barrier curve but differing only in magnitude. Combinations of opposite and unequal charges also have the capacity to emulate or model quark “confinement.” Like the Coulomb barrier, confinement is a quantum mechanical phenomenon. Nothing like it exists in the classical domain. And like the Coulomb barrier, confinement forces may be modeled with an appropriately configured sequence of alternating and unequal charges, as shown in Figure 3(a). Here, the six alternating +1 and -2 coulomb charges are assumed to occupy fixed positions 1 cm apart. A displacement force is applied to an internal -2 charge in a direction orthogonal to the linear sequence. The orthogonal force component between the internal -2 charge and each of the other charges in the sequence is then determined using Coulomb's law. The sum of these forces is plotted versus the distance between the displaced charge and its original in-line position (see Figure 3(b)). The plot is undeniably electrostatic and yet bears no resemblance to the inverse square plot normally associated with the force between a pair of charged particles. In fact, this electrostatic force/distance curve more closely resembles published quark “confinement" force behavior.