Semi-discrete optimal transport methods for the semi-geostrophic equations

We give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinates, for arbitrary initial measures with compact support. This new proof, based on semi-discrete optimal transport techniques, works by characterising discrete solutions of SG in geostrophic coordinates in terms of trajectories satisfying an ordinary differential equation. It is advantageous in its simplicity and its explicit relation to Eulerian coordinates through the use of Laguerre tessellations. Using our method, we obtain improved time-regularity for a large class of discrete initial measures, and we compute explicitly two discrete solutions. The method naturally gives rise to an efficient numerical method, which we illustrate by presenting simulations of a 2-dimensional semi-geostrophic flow in geostrophic coordinates generated using a numerical solver for the semi-discrete optimal transport problem coupled with an ordinary differential equation solver.

A Novel Dual-Band Implantable Antenna for Pancreas Telemetry Sensor Applications

In this study, a novel implantable dual-band planar inverted F-antenna (PIFA) is proposed and designed for wireless biotelemetry. The developed antenna is intended to operate on the surface of the pancreas within the Medical Device Radiocommunications Service (MedRadio 401–406 MHz) and the industrial scientific and medical band (ISM, 2.4–2.5 GHz). The design analysis was carried out in two steps, initially inside a canonical model representing the pancreas, based on a finite element method (FEM) numerical solver. The proposed antenna was further simulated inside the human body taking into account the corresponding dimensions of the tissues and the electrical properties at the frequencies of interest using a finite-difference time-domain (FDTD) numerical solver. Resonance, radiation performance, electrical field attenuation, total radiated power, and specific absorption rate (SAR), which determines the safety of the patient and the maximum permissible input power and other electromagnetic parameters, are presented and evaluated.

Methodology for composite materials shrinkage definition for use in shipbuilding and marine technology

Deformations of steel material in shipbuilding and marine technology applications as a result of mechanical or temperature influences are a well-known problem. However, in the modern shipbuilding industry, the application of alternative materials, especially composite materials, in the structure and for the equipment of the ship is increasingly represented. Consequently, there is a need to determine the deformation and change of characteristics of such composite materials as a result of various mechanical, and especially temperature influences that cause the so-called shrinkage. The basic composite production process involves connecting the matrix with a catalyst and accelerators that create temperature, then the material shrinks by cooling when it can change its dimensions and characteristics. Also, in order to achieve the best possible mechanical properties, composite materials are specially heated and then cooled according to strictly defined processes and curves. The ability to predict the characteristics and parameters of such deformations is important in the context of the application of composite materials. To define such deformations, different methods are used within individual numerical solvers, whose results can differ significantly from each other. Therefore, the authors in this paper present an established methodology for predicting mechanical and temperature deformations, and modelling of composite materials, based on the analysis of analytical methods and numerical solvers with the aim of defining the most accurate numerical solver. By applying the presented methodology, it is expected to raise the level of accuracy and quality of composite materials production as well as to raise the quality of design solutions and efficiency of production procedures during shipbuilding in particular, but also within different marine technology applications and during the product’s life cycle.

Modeling Brownian Microparticle Trajectories in Lab-on-a-Chip Devices with Time Varying Dielectrophoretic or Optical Forces

Lab-on-a-chip (LOC) devices capable of manipulating micro/nano-sized samples have spurred advances in biotechnology and chemistry. Designing and analyzing new and more advanced LOCs require accurate modeling and simulation of sample/particle dynamics inside such devices. In this work, we present a generalized computational physics model to simulate particle/sample trajectories under the influence of dielectrophoretic or optical forces inside LOC devices. The model takes into account time varying applied forces, Brownian motion, fluid flow, collision mechanics, and hindered diffusion caused by hydrodynamic interactions. We develop a numerical solver incorporating the aforementioned physics and use it to simulate two example cases: first, an optical trapping experiment, and second, a dielectrophoretic cell sorter device. In both cases, the numerical results are found to be consistent with experimental observations, thus proving the generality of the model. The numerical solver can simulate time evolution of the positions and velocities of an arbitrarily large number of particles simultaneously. This allows us to characterize and optimize a wide range of LOCs. The developed numerical solver is made freely available through a GitHub repository so that researchers can use it to develop and simulate new designs.

Research on the effect of car’s roll motion on the aerodynamic characteristics of high-speed car

The main purpose of this study is to study the aerodynamic mechanism of periodic roll motion of car body and provide engineering reference for car design and safety evaluation. A simplified roll motion model is established based on a real car model. The two-wheel centerline of the left-wheel symmetrical section is considered as the roll axis, and the overset mesh method was used to model the sinusoidal roll motion of the car. According to the experimental data, the frequency and maximum roll angle were set to be 10 Hz and 2.2°, respectively. A transient numerical solver based on the detached-eddy simulation method is employed. The accuracy of the numerical method is validated by means of the wind tunnel test. Due to the asymmetry of the movement, the aerodynamic change of the roll motion was obvious. It is found that the roll motion is closely related to the aerodynamic characteristics of the car. Because of the hysteresis effect, the phase of aerodynamic force on the car shifts and the most dangerous position of the car is obtained. In addition, the aerodynamic differences of the car parts are found, and the wake is analyzed in detail.

UBER v1.0: a universal kinetic equation solver for radiation belts

Recent proceedings in radiation belt studies have proposed new requirements for numerical methods to solve the kinetic equations involved. In this article, we present a numerical solver that can solve the general form of the radiation belt Fokker–Planck equation and Boltzmann equation in arbitrarily provided coordinate systems and with user-specified boundary geometry, boundary conditions, and equation terms. The solver is based upon the mathematical theory of stochastic differential equations, whose computational accuracy and efficiency are greatly enhanced by specially designed adaptive algorithms and a variance reduction technique. The versatility and robustness of the solver are exhibited in four example problems. The solver applies to a wide spectrum of radiation belt modeling problems, including the ones featuring non-diffusive particle transport such as that arising from nonlinear wave–particle interactions.

Flow Dynamics of the Homogeneous and Heterogeneous Reactions with an Internal Heat Generation and Thermal Radiation between Two Squeezing Plates

This paper explores the time dependent squeezing flow of a viscous fluid between parallel plates with internal heat generation and homogeneous/heterogeneous reactions. The motive of the present effort is to upgrade the heat transformation rate for engineering and industrial purpose with the rate of chemical reaction. For this purpose the equations for the conservation of mass, momentum, energy and homogeneous/heterogeneous reactions are transformed to a system of coupled equations using the similarity transformation. According to HAM, with the proper starting assumptions and other factors, a similarity solution may be found. On the way to verifying the validity and correctness of HAM findings, we compare the HAM solution with numerical solver programme BVP4c to see whether it matches up. The results of a parametric inquiry are summarized and presented with the use of graphs.