Computer 3D-simulation of the temperature and diffusion kinetics of SHS in the closest packing of Ni@Al “core-shell” mesocells for modes with variable values of the key ignition parameters

The paper presents the results of computer 3D-simulation of the temperature and diffusion kinetics of SHS in a test model cluster of Ni-Al particles for modes with variable values of the key parameters of the SHS combustion wave ignition. The key parameters for the SHS combustion wave ignition were chosen as follows: the initial temperature for preliminary heating of the Ni-Al particles mixture, the ignition temperature of the combustion wave in the mixture of Ni-Al particles, the duration of the action of the heat pulse until the combustion wave ignition, and the thickness of the ignited layer in the mixture of particles. A program has been created to generate a test model cluster in the form of the closest ball packing of the Ni@Al “core-shell” mesocells (CBP-structure cluster of the Ni@Al “core-shell” mesocells). Using such a CBP-structure cluster, was continued a testing of created software package intended for 3D-simulation of SHS macrokinetics in a heterogeneous particle mixture, taking into account parallel MPI-calculations. In addition, the value ranges of the key parameters of the SHS combustion wave ignition for which the simulation results are in adequate agreement with the experimental data are determined as the parameters of the program model for SHS-simulation. The results of computational experiments have shown that diffusion kinetics is interrelated with temperature kinetics, and in mesocells with different locations within the CBP-structure cluster, the formation of intermetallic phases occurs inhomogeneously.

Direct modifications of tetrahedral meshes

Purpose During the industrial design process, a product is usually modified and analyzed repeatedly until reaching the final design. Modifying the model and regenerating a mesh for every update during this process is very time consuming. To improve efficiency, it is necessary to circumvent the computer-aided design modeling stage when possible and directly modify the meshes to save valuable time. The purpose of this paper is to develop a method for mesh modifications. Design/methodology/approach In contrast to existing studies, which focus on one or a class of modifications, this paper comprehensively studies mesh union, mesh gluing, mesh cutting and mesh partitioning. To improve the efficiency of the method, the paper presents a fast and effective surface mesh remeshing algorithm based on a ball-packing method and controls the remeshing regions with a size field. Findings Examples and results show that the proposed mesh modification method is efficient and effective. The proposed method can be also applied to meshes with different material properties, which is very different with previous work that is only suitable for the meshes with same material property. Originality/value This paper proposes an efficient and comprehensive tetrahedral mesh modification method, through which engineers can directly modify meshes instead of models and save time.

Kottman’s constant, packing constant and Riesz angle in some classes of K ¨othe sequence spaces

We have found a sufficient condition in order that the Kottman constant to be equal to the Riesz angle for Kothe ¨ sequence spaces. We have found the ball packing constant in weighted Orlicz sequence spaces, endowed with Luxemburg or p–Amemiya norm. We have calculated the Riesz angle for Musielak–Orlicz, Nakano, weighted Orlicz, Orlicz, Orlicz–Lorentz, Lorentz and Cesaro sequence spaces.

Pemodelan perpindahan massa ekstraksi kolom isian dengan distribusi ukuran tetesan

Mass transfer modeling of extraction in a packed bed with droplet size distribution The evaluation of liquid extraction packed column is not able yet to give a satisfying result caused by constant spherical droplet size assumption. Droplet size from dispersion phase that is not homogeneous causes column calculation approach with assumption form of droplet haves the character of constant cannot be applied again. The goal of this research is to build droplet distribution model and mass transfer model at various heights of extraction column both in continuous phase and in dispersion phase. Droplet distribution model is more accurately applied to describe droplet breaks distribution for extraction in glass ball packed column with average of errors 4.53% compared to raschig ring packed column with average error of 11.52 %. At glass ball packing, the mass transfer modeling with total droplet has errors average to 57.67% while at raschig ring packing the model has errors average to 121.38%. Glass ball packing column model has smaller mean errors compared to raschig ring packing column because the glass ball packing form is more regular than the raschig ring packing. The amount of error between the mass transfer models and the experiment is caused by difference of the initial number of droplets that exit from the nozzle in the half circle column and in the full circle column. Keyword: extraction, packed column, droplet distribution model, mass transfer model AbstrakUkuran tetesan dari fasa dispersi yang tidak homogen menyebabkan pendekatan perhitungan kolom dengan asumsi bentuk tetesan bersifat konstan tidak dapat digunakan lagi. Tujuan dari penelitian ini adalah untuk membangun model distribusi tetesan dan model perpindahan massa pada berbagai ketinggian kolom ekstraksi baik di fasa kontinu maupun di fasa dispersi. Model distribusi tetesan lebih tepat digunakan untuk memodelkan fraksi tetesan pecah hasil penelitian pada ekstraksi kolom isian bola kaca dengan rata-rata error sebesar 4,53% dibandingkan dengan kolom isian raschig ring yang mempunyai error sebesar 11,52 Pada isian bola kaca pemodelan perpindahan massa dengan tetesan total mempunyai error rata-rata sebesar 57,67% sedangkan pada isian raschig ring mempunyai error rata-rata sebesar 121,38%. Model kolom isian bola kaca mempunyai error rata-rata yang lebih kecil dibandingkan dengan kolom kolom isian raschig ring, dikarenakan model isian bola kaca bentuknya lebih beraturan dibanding dengan kolom isian raschig ring yang bentuknya lebih tidak beraturan. Besarnya error perpindahan massa antara model dengan percobaan disebabkan oleh tidak samanya jumlah tetesan awal pada kolom setengah lingkaran dengan jumlah tetesan awal pada kolom lingkaran penuh.Kata kunci : ekstraksi,kolom isian, model distribusi tetesan, model perpindahan massa

Top dense hyperbolic ball packings and coverings for complete coxeter orthoscheme groups

In n-dimensional hyperbolic space Hn (n > 2), there are three types of spheres (balls): the sphere, horosphere and hypersphere. If n = 2, 3 we know a universal upper bound of the ball packing densities, where each ball?s volume is related to the volume of the corresponding Dirichlet-Voronoi (D-V) cell. E.g., in H3 a densest (not unique) horoball packing is derived from the {3,3,6} Coxeter tiling consisting of ideal regular simplices T? reg with dihedral angles ?/3. The density of this packing is ??3 ? 0.85328 and this provides a very rough upper bound for the ball packing densities as well. However, there are no ?essential" results regarding the ?classical" ball packings with congruent balls, and for ball coverings either. The goal of this paper is to find the extremal ball arrangements in H3 with ?classical balls". We consider only periodic congruent ball arrangements (for simplicity) related to the generalized, so-called complete Coxeter orthoschemes and their extended groups. In Theorems 1.1 and 1.2 we formulate also conjectures for the densest ball packing with density 0.77147... and the loosest ball covering with density 1.36893..., respectively. Both are related with the extended Coxeter group (5,3,5) and the so-called hyperbolic football manifold. These facts can have important relations with fullerenes in crystallography.

Even More Infinite Ball Packings from Lorentzian Root Systems

Boyd (1974) proposed a class of infinite ball packings that are generated by inversions. Later, Maxwell (1983) interpreted Boyd's construction in terms of root systems in Lorentz spaces. In particular, he showed that the space-like weight vectors correspond to a ball packing if and only if the associated Coxeter graph is of "level 2"'. In Maxwell's work, the simple roots form a basis of the representations space of the Coxeter group. In several recent studies, the more general based root system is considered, where the simple roots are only required to be positively independent. In this paper, we propose a geometric version of "level'' for root systems to replace Maxwell's graph theoretical "level''. Then we show that Maxwell's results naturally extend to the more general root systems with positively independent simple roots. In particular, the space-like extreme rays of the Tits cone correspond to a ball packing if and only if the root system is of level $2$. We also present a partial classification of level-$2$ root systems, namely the Coxeter $d$-polytopes of level-$2$ with $d+2$ facets.