Search

Boxing and related sports activities have become a standard workout regime at many fitness studios worldwide. Oftentimes, people are interested in the calories expended during these workouts. This note focuses on determining the calories in a boxer's jab, using kinematic vector-loop relations and basic work–energy principles. Numerical simulations are undertaken to illustrate the basic model. Multi-limb extensions of the model are also discussed.

Rapid, energy-efficient sintering of materials comprised heterogeneous powders is of critical importance in emerging technologies where traditional manufacturing processes may be difficult to apply. In particular, electrically aided sintering, which uses the material's inherent resistance to flowing current—resulting in Joule heating to bond the powder components—has great promise because it produces desired materials without much post-processing. Furthermore, it has advantages over other methods, such as high purity of processed materials, in particular, because there are few steps during the approach. In order to electrically process the material properly, one must ascertain the externally applied field to properly Joule heat the various material components in the powder mixture. The Joule-heating field is mathematically expressed by the inner product ( J ⋅ E ) of the current ( J ) and electric ( E ) fields throughout the system. This study develops estimates for the Joule-heating fields carried by each phase in a powder mixture, using knowledge of only the externally applied current, and the material properties of the components comprising the mixture. These estimates are useful in guiding and reducing time-consuming material synthesis involving laboratory experiments and/or large-scale numerical simulation.

In modern advanced manufacturing processes, such as three-dimensional printing of electronics, fine-scale particles are added to a base fluid yielding a modified fluid. For example, in three-dimensional printing, particle-functionalized inks are created by adding particles to freely flowing solvents forming a mixture, which is then deposited onto a surface, which upon curing yields desirable solid properties, such as thermal conductivity, electrical permittivity and magnetic permeability. However, wear at solid–fluid interfaces within the machinery walls that deliver such particle-laden fluids is typically attributed to the fluid-induced shear stresses, which increase with the volume fraction of added particles. The objective of this work is to develop a rigorous strict upper bound for the tolerable volume fraction of particles that can be added, while remaining below a given stress threshold at a fluid–solid interface. To illustrate the bound’s utility, the expression is applied to a series of classical flow regimes.

A computational framework is developed which couples a series of models, each describing vastly different physical events, in order to characterize particle growth (agglomeration) in thermochemically reacting granular flows. The modelling is purposely simplified to expose the dominant mechanisms which control agglomeration. The overall system is comprised of relatively simple coupled submodels describing impact, heat production, bonding and fragmentation, each of which can be replaced by more elaborate descriptions, if and when they are available. Inverse problems, solved with a genetic algorithm, are then constructed to ascertain system parameters which maximize agglomeration likelihood within a range of admissible data.

The compaction of cohesive hyperelastic polymeric granules is investigated. Finite strain concentration functions are developed for material models of compressible Mooney Rivlin type, which allow one to analytically estimate, in fact rigorously bound, the progressive reduction of the volume fraction of the porous gap between the granules as a function of increasing applied loading.

There exists a variety of difficulties in the computational design of macroscopic solid material properties formed by doping a homogeneous base matrix material with randomly distributed particles having different properties. Three primary problems are (1) the wide array of free microdesign variables, such as particle topology, property phase contrasts and volume fraction, which render the associated objective functions to be highly non-convex; (2) that the associated objective functions are not differentiable with respect to design variables, primarily due to prescribed constraints, such as prespecified restrictions on the microscale stress-field behaviour; and (3) the effective responses of various finite-sized samples, of equal volume but of different random particle distributions, exhibit mutual fluctuations, leading to amplified noise in optimization strategies where objective function sensitivities or comparisons are needed. The focus of this paper is the development of a statistical genetic algorithm which can handle difficulties due to non-convexity, lack of regularity and size effects. Theoretical properties of the overall approach are investigated. Semi-analytical and large-scale numerical examples, involving finite-element type discretizations, are given to illustrate its practical application.

In this paper, a mathematical model is developed to qualitatively simulate the progressive time-evolution of a blast from a simple firework. Estimates are made for the blast radius that one can expect for a given amount of detonation energy and pyrotechnic display material. The model balances the released energy from the initial blast pulse with the subsequent kinetic energy and then computes the trajectory of the material under the influence of the drag from the surrounding air, gravity and possible buoyancy. Under certain simplifying assumptions, the model can be solved for analytically. The solution serves as a guide to identifying key parameters that control the evolving blast envelope. Three-dimensional examples are given.

The goal of this work is to develop a computational framework to rapidly simulate the light scattering response of multiple red blood cells. Because the wavelength of visible light (3.8×10 −7 m≤ λ ≤7.2×10 −7 m) is approximately an order of magnitude smaller than the diameter of a typical red blood cell scatterer ( d ≈8×10 −6 m), geometric ray-tracing theory is applicable, and can be used to quickly ascertain the amount of optical energy, characterized by the Poynting vector, that is reflected and absorbed by multiple red blood cells. The overall objective is to provide a straightforward approach that can be easily implemented by researchers in the field, using standard desktop computers. Three-dimensional examples are given to illustrate the approach and the results compare quite closely to experiments on blood samples conducted at the Children's Hospital Oakland Research Institute (CHORI).

The accumulation of microscale materials at solid–fluid interfaces in biological channels is often the initial stage of certain growth processes, which are present in some forms of atherosclerosis. The objective of this work is to develop a relatively simple model for such accumulation, which researchers can use to qualitatively guide their analyses. Specifically, the approach is to construct rate equations for the accumulation at the solid–fluid interface as a function of the intensity of the shear stress. The accumulation of material subsequently reduces the cross-sectional area of the channel until the fluid-induced shear stress at the solid–fluid interface reaches a critical value, which terminates the accumulation rate. Characteristics of the model are explored analytically and numerically.