Parcel Eulerian-Lagrangian fluid dynamics for rotating geophysical flows

Parcel Eulerian-Lagrangian Hamiltonian formulations have recently been used in structure-preserving numerical schemes, asymptotic calculations and in alternative explanations of fluid parcel (in) stabilities. A parcel formulation describes the dynamics of one fluid parcel with a Lagrangian kinetic energy but an Eulerian potential evaluated at the parcel's position. In this paper, we derive the geometric link between the parcel Eulerian-Lagrangian formulation and well-known variational and Hamiltonian formulations for three models of ideal and geophysical fluid flow: generalized two-dimensional vorticity-stream function dynamics, the rotating two-dimensional shallow-water equations and the rotating three-dimensional compressible Euler equations

Thermal Modeling in Polymer Extrusion

In this paper we consider thermal effects of polymer flows through a cylindrical die. First, we derive a model for the oscillatory behavior of polymer flow in an extruder given a functional relation between the pressure and flow rate. A simple isothermal but temperature dependent model is constructed to find this relation. Unfortunately, the model is shown to be invalid in the physical regime of interest. We present several arguments to suggest that the isothermal assumption is reasonable but that a more detailed understanding of the small-scale molecular dynamics near the boundary may be required. Second, we show that a simplified model for thermoflow multiplicity in a cooled tube is inconsistent, when the stationary non-Newtonian flow is assumed to be incompressible without radial pressure gradients and without radial velocity. This inconsistency can be removed by allowing for weak compressibility effects in the down-steam area

Reservoir formation in shallow granular flows through a contraction

We consider flow of dry granular matter down an inclined chute with a localized contraction. Measurements and analysis show that changes in particle volume fraction are important, especially across granular bores. For fixed upstream conditions and depending on the nozzle width of the contraction, we observe either small oblique jumps, a reservoir with a steady jump, or a reservoir with an upstream traveling bore. Shallow layer theory extended to include porosity changes qualitatively predicts these regimes. Implications for volcanic debris \ud ows are discussed

Using Social Network Analysis to gain insight into social creativity while designing digital mathematics books

Analysing the processes and products of creativity to better understand and support individuals and teams, is a difficult and elusive challenge despite years of research in creativity. In this article, we are particularly interested in social creativity in communities of interest. Building on Guilford's classic model of Divergent Thinking of fluency, flexibility, originality and elaboration, we employ Social Network Analysis to model the creative design process. The creative process in the current study takes place in a technological environment called the ‘MC-squared platform’, in which members of a community of interest collaborate in a social, co-creative process for designing digital, mathematical textbooks. Both the technological environment and the methodology are exemplified through two case examples, one on the design process of a digital book about a bioclimatic amusement park and one on the design process of a digital book about fractions. We conclude that, for these examples, both the technological tool and the data analysis approach provide insight into the social creativity process of the community of interest

Breaking waves on a dynamic Hele-Shaw beach

We report the formation of quasi-steady beaches and dunes via breaking waves in our tabletop ‘Hele-Shaw’ beach experiment. Breaking waves are generated by a wave maker, and zeolite particles act as sand. The tank is narrow, just over one-particle diameter wide, creating a quasi-2D set-up. Classical breaker types are observed on a time-scale of about a second. Beach formation under breakers occurs on a longer time-scale, and is a matter of minutes for a range of mono-chromatic wave frequencies. Alternating the wave maker motion between two frequencies generally leads to beach formation but occasionally to formation of a stable dune with water on either side. Finally, the Hele-Shaw configuration explored here experimentally lends itself to multi-scale modeling of beach dynamics

Revisiting Hele-Shaw dynamics to better understand beach evolution

Wave action, particularly during storms, drives the evo lution of beaches. Beach evolution by non-linear break ing waves is poorly understood due to its three-dimensional character, the range of scales involved, and our limited understanding of particle-wave interactions. We show how a novel, three-phase extension to the classic “Hele-Shaw” laboratory experiment can be designed that creates beach morphologies with breaking waves in a quasi-two-dimensional setting. Our thin Hele-Shaw cell simplifies the inherent complexity of three-phase dynamics: all dynamics become clearly visible and measurable. We show that beaches can be created in tens of minutes by several types of breaking waves, with about one-second periods. Quasi-steady beach morphologies emerge as function of initial water depth, at-rest bed level and wave-maker frequency. These are classified mathematically and lead to beaches, berms and sand bars

A Cost-Effectiveness Protocol for Flood-Mitigation Plans Based on Leeds’ Boxing Day 2015 Floods

Inspired by the Boxing Day 2015 flood of the River Aire in Leeds, UK, and subsequent attempts to mitigate adverse consequences of flooding, the goals considered are: (i) to revisit the concept of flood-excess volume (FEV) as a complementary diagnostic for classifying flood events; (ii) to establish a new roadmap/protocol for assessing flood-mitigation schemes using FEV; and, (iii) to provide a clear, graphical cost-effectiveness analysis of flood mitigation, exemplified for a hypothetical scheme partially based on actual plans. We revisit the FEV concept and present it as a three-panel graph using thresholds and errors. By re-expressing FEV as a 2m -deep square lake of equivalent capacity, one can visualise its dimensions in comparison with the river valley considered. Cost-effectiveness of flood-mitigation measures is expressed within the FEV square-lake; different scenarios of our hypothetical flood-mitigation scheme are then presented and assessed graphically, with each scenario involving a combination, near and further upstream of Leeds, of higher (than existing) flood-defence walls, enhanced flood-plain storage sites, giving-room-to-the-river bed-widening and natural flood management. Our cost-effectiveness analysis is intended as a protocol to compare and choose between flood-mitigation scenarios in a quantifiable and visual manner, thereby offering better prospects of being understood by a wide audience, including citizens and city-council planners. Using techniques of data analysis combined with general river hydraulics, common-sense and upper-bound estimation, we offer an accessible check of flood-mitigation plans

Modeling and simulation of phase-transitions in multicomponent aluminum alloy casting

The casting process of aluminum products involves the spatial distribution of alloying elements. It is essential that these elements are uniformly distributed in order to guarantee reliable and consistent products. This requires a good understanding of the main physical mechanisms that affect the solidification, in particular the thermodynamic description and its coupling to the transport processes of heat and mass that take place. The continuum modeling is reviewed and methods for handling the thermodynamics component of multi-element alloys are proposed. Savings in data-storage and computing costs on the order of 100 or more appear possible, when a combination of data-reduction and data-representation methods is used. To test the new approach a simplified model was proposed and shown to qualitatively capture the evolving solidification front

Some studies on the deformation of the membrane in an RF MEMS switch

Radio Frequency (RF) switches of Micro Electro Mechanical Systems (MEMS) are appealing to the mobile industry because of their energy efficiency and ability to accommodate more frequency bands. However, the electromechanical coupling of the electrical circuit to the mechanical components in RF MEMS switches is not fully understood. In this paper, we consider the problem of mechanical deformation of electrodes in RF MEMS switch due to the electrostatic forces caused by the difference in voltage between the electrodes. It is known from previous studies of this problem, that the solution exhibits multiple deformation states for a given electrostatic force. Subsequently, the capacity of the switch that depends on the deformation of electrodes displays a hysteresis behaviour against the voltage in the switch. We investigate the present problem along two lines of attack. First, we solve for the deformation states of electrodes using numerical methods such as finite difference and shooting methods. Subsequently, a relationship between capacity and voltage of the RF MEMS switch is constructed. The solutions obtained are exemplified using the continuation and bifurcation package AUTO. Second, we focus on the analytical methods for a simplified version of the problem and on the stability analysis for the solutions of deformation states. The stability analysis shows that there exists a continuous path of equilibrium deformation states between the open and closed state

Numerical Experiments on Extreme Waves Through Oblique–Soliton Interactions

Extreme water-wave motion is investigated analytically and numerically by considering two-soliton and three-soliton interactions on a horizontal plane. We successfully determine numerically that soliton solutions of the unidirectional Kadomtsev–Petviashvili equation (KPE), with equal far-field individual amplitudes, survive reasonably well in the bidirectional and higher-order Benney–Luke equations (BLE). A well-known exact two-soliton solution of the KPE on the infinite horizontal plane is used to seed the BLE at an initial time, and we confirm that the KPE-fourfold amplification approximately persists. More interestingly, a known three-soliton solution of the KPE is analysed further to assess its eight- or ninefold amplification, the latter of which exists in only a special and difficult-to-attain limit. This solution leads to an extreme splash at one point in space and time. Subsequently, we seed the BLE with this three-soliton solution at a suitable initial time to establish the maximum amplification: it is approximately 7.8 for a KPE amplification of 8.4. Herein, the computational domain and solutions are truncated approximately to a fully periodic or half-periodic channel geometry of sufficient size, essentially leading to cnoidal-wave solutions. Moreover, special geometric (finite-element) variational integrators in space and time have been used in order to eradicate artificial numerical damping of, in particular, wave amplitude