Simulation of the Marangoni Effect and Phase Change Using the Particle Finite Element Method

A simulation method is developed herein based on the particle finite element method (PFEM) to simulate processes with surface tension and phase change. These effects are important in the simulation of industrial applications, such as welding and additive manufacturing, where concentrated heat sources melt a portion of the material in a localized fashion. The aim of the study is to use this method to simulate such processes at the meso-scale and thereby gain a better understanding of the physics involved. The advantage of PFEM lies in its Lagrangian description, allowing for automatic tracking of interfaces and free boundaries, as well as its robustness and flexibility in dealing with multiphysics problems. A series of test cases is presented to validate the simulation method for these two effects in combination with temperature-driven convective flows in 2D. The PFEM-based method is shown to handle both purely convective flows and those with the Marangoni effect or melting well. Following exhaustive validation using solutions reported in the literature, the obtained results show that an overall satisfactory simulation of the complex physics is achieved. Further steps to improve the results and move towards the simulation of actual welding and additive manufacturing examples are pointed out.

Double rotations of cylinders on thermosolutal convection of a wavy porous medium inside a cavity mobilized by a nanofluid and impacted by a magnetic field

Purpose The purpose of this paper is to work out the magnetic forces on heat/mass transmission in a cavity filled with a nanofluid and wavy porous medium by applying the incompressible smoothed particle hydrodynamics (ISPH) method. Design/methodology/approach The cavity is filled by a nanofluid and an undulating layer of a porous medium. The inserted two circular cylinders are rotated around the cavity’s center by a uniform circular velocity. The outer circular cylinder has four gates, and it carries two different boundary conditions. The inner circular cylinder is carrying Th and Ch. The Lagrangian description of the dimensionless regulating equations is solved numerically by the ISPH method. Findings The major outcomes of the completed numerical simulations illustrated the significance of the wavy porous layer in declining the nanofluid movements, temperature and concentration in a cavity. The nanofluid movements are declining by an increase in nanoparticle parameter and Hartmann number. The variations on the boundary conditions of an outer circular cylinder are changing the lineaments of heat/mass transfer in a cavity. Originality/value The originality of this study is investigating the dual rotations of the cylinders on magnetohydrodynamics thermosolutal convection of a nanofluid in a cavity saturated by two wavy horizontal porous layers.

Minimum Entropy Production Effect on a Quantum Scale

The discovery of quantized electric conductance by the group of van Wees in 1988 was a major breakthrough in physics. A decade later, the group of Schwab has proven the existence of quantized thermal conductance. Advancing from these and many other aspects of the quantized conductances in other phenomena of nature, the concept of quantized entropy current can be established and it eases the description of a transferred quantized energy package. This might yield a universal transport behavior of the microscopic world. During the transfer of a single energy quantum, hν, between two neighboring domains, the minimum entropy increment is calculated. It is pointed out that the possible existence of the minimal entropy transfer can be formulated. Moreover, as a new result, it is proved that this minimal entropy transfer principle is equivalent to the Lagrangian description of thermodynamics.

Numerical Investigation of Cloud Cavitation and Its Induced Shock Waves

This paper numerically investigates unsteady behavior of cloud cavitation, in particular, to elucidate the induced shock wave emission. To do this, we consider a submerged water-jet injection into still water through a nozzle and make some numerical analysis of two-dimensional multiphase flows by Navier-Stokes equations. In our previous study [7], we have shown that twin vortices symmetrically appear in the injected water, which plays an essential role in performing the unsteady behavior of a cloud of bubbles. In this paper, we further illustrate the elementary process of the emission of the shock waves. First, we set up the mixture model of liquid and gas in Lagrangian description by the SPH method, together with the details on the treatment of boundary conditions. Second, we show the velocity fields of the multiphase flow to illustrate the inception, growth as well as the collapse of the cloud. In particular, we explain the mechanism of the collapse of the cloud in view of the motion of the twin vortices. Further, we investigate the pressure fields of the multiphase flow in order to demonstrate how the shock wave is emitted associated with the collapse of the cloud. Finally, we show that a small shock wave may be released prior to the main shock wave emission.

Conformal manifolds and 3d mirrors of Argyres-Douglas theories

Argyres-Douglas theories constitute an important class of superconformal field theories in 4d. The main focus of this paper is on two infinite families of such theories, known as $$ {D}_p^b $$ D p b (SO(2N)) and (Am, Dn). We analyze in depth their conformal manifolds. In doing so we encounter several theories of class 𝒮 of twisted Aodd, twisted Aeven and twisted D types associated with a sphere with one twisted irregular puncture and one twisted regular puncture. These models include Dp(G) theories, with G non-simply-laced algebras. A number of new properties of such theories are discussed in detail, along with new SCFTs that arise from partially closing the twisted regular puncture. Moreover, we systematically present the 3d mirror theories, also known as the magnetic quivers, for the $$ {D}_p^b $$ D p b (SO(2N)) theories, with p ≥ b, and the (Am, Dn) theories, with arbitrary m and n. We also discuss the 3d reduction and mirror theories of certain $$ {D}_p^b $$ D p b (SO(2N)) theories, with p < b, where the former arises from gauging topological symmetries of some $$ {T}_p^{\sigma } $$ T p σ [SO(2M)] theories that are not manifest in the Lagrangian description of the latter.

Scattering amplitudes for monopoles: pairwise little group and pairwise helicity

On-shell methods are particularly suited for exploring the scattering of electrically and magnetically charged objects, for which there is no local and Lorentz invariant Lagrangian description. In this paper we show how to construct a Lorentz-invariant S-matrix for the scattering of electrically and magnetically charged particles, without ever having to refer to a Dirac string. A key ingredient is a revision of our fundamental understanding of multi-particle representations of the Poincaré group. Surprisingly, the asymptotic states for electric-magnetic scattering transform with an additional little group phase, associated with pairs of electrically and magnetically charged particles. The corresponding “pairwise helicity” is identified with the quantized “cross product” of charges, e1g2− e2g1, for every charge-monopole pair, and represents the extra angular momentum stored in the asymptotic electromagnetic field. We define a new kind of pairwise spinor-helicity variable, which serves as an additional building block for electric-magnetic scattering amplitudes. We then construct the most general 3-point S-matrix elements, as well as the full partial wave decomposition for the 2 → 2 fermion-monopole S-matrix. In particular, we derive the famous helicity flip in the lowest partial wave as a simple consequence of a generalized spin-helicity selection rule, as well as the full angular dependence for the higher partial waves. Our construction provides a significant new achievement for the on-shell program, succeeding where the Lagrangian description has so far failed.

More views of a one-sided surface: mechanical models and stereo vision techniques for Möbius strips

Möbius strips are prototypical examples of ribbon-like structures. Inspecting their shapes and features provides useful insights into the rich mechanics of elastic ribbons. Despite their ubiquity and ease of construction, quantitative experimental measurements of the three-dimensional shapes of Möbius strips are surprisingly non-existent in the literature. We propose two novel stereo vision-based techniques to this end—a marker-based technique that determines a Lagrangian description for the construction of a Möbius strip, and a structured light illumination technique that furnishes an Eulerian description of its shape. Our measurements enable a critical evaluation of the predictive capabilities of mechanical theories proposed to model Möbius strips. We experimentally validate, seemingly for the first time, the developable strip and the Cosserat plate theories for predicting shapes of Möbius strips. Equally significantly, we confirm unambiguous deficiencies in modelling Möbius strips as Kirchhoff rods with slender cross-sections. The experimental techniques proposed and the Cosserat plate model promise to be useful tools for investigating a general class of problems in ribbon mechanics.

MPM–FEM hybrid method for granular mass–water interaction problems

The present study proposes an MPM (material point method)–FEM (finite element method) hybrid analysis method for simulating granular mass–water interaction problems, in which the granular mass causes dynamic motion of the surrounding water. While the MPM is applied to the solid (soil) phase whose motion is suitably represented by Lagrangian description, the FEM is applied to the fluid (water) phase that is adapted for Eulerian description. Also, the phase-field approach is employed to capture the free surface. After the accuracy of the proposed method is tested by comparing the results to some analytical solutions of the consolidation theory, several numerical examples are presented to demonstrate its capability in simulating fluid motions induced by granular mass movements.

A Sequential Approach for Simulation of Thermoforming and Squeeze Flow of Glass Mat Thermoplastics

In this study, a sequential thermoforming and squeeze flow simulation approach for Glass Mat Thermoplastic (GMT) material is proposed and applied to a hat section geometry using input properties based upon Tepex flowcore, a long glass fiber reinforced polyamide (PA/GF) mat manufactured by Lanxess. First, a fully-coupled thermomechanical simulation is conducted based on a purely Lagrangian description, to efficiently capture thermoforming. Subsequently, relevant state variables are mapped and initialized for a Coupled-Eulerian-Lagrangian (CEL) approach. The CEL approach is adopted to accurately capture squeeze flow, which is not possible by a purely Lagrangian description. While numerical techniques differ, both approaches use the same three-dimensional and thermomechanical constitutive equations including an equation of state, a nonlinear viscosity model, and crystallization kinetics, implemented through a material user-subroutine (VUMAT) for the commercially available simulation software package ABAQUS/Explicit.