An Optimal Estimate for the Anisotropic Logarithmic Potential

This paper introduces the new annulus body to establish the optimal lower bound for the anisotropic logarithmic potential as the complement to the theory of its upper bound estimate which has already been investigated. The connections with convex geometry analysis and some metric properties are also established. For the application, a polynomial dual log-mixed volume difference law is deduced from the optimal estimate.

The Lp-mixed quermassintegrals for 0 < p < 1

In the paper, Lp-harmonic addition, p-harmonic Blaschke addition and Lp-dual mixed volume are improved. A new p-harmonic Blaschke mixed quermassintegral is introduced. The relationship between p-harmonic Blaschke mixed volume and Lp-dual mixed volume is shown.

Respon Tanaman Pakcoy (Brassica rapa L.) Pada Beberapa Media Tumbuh Organik

AbstrakMedia tanam adalah bagian dari faktor penting untuk menentukan perkembangan dan pertumbuhan tanaman. Kualitasnya sangat menentukan produktivitas tanaman. Penelitian ini bertujuan mengkaji pengaruh kombinasi beberapa material organik, yaitu arang sekam, kompos, dan rabuk kandang buangan kambing sebagai media tanam terhadap pertumbuhan dan hasil tanaman pakcoy dan menentukan kombinasi material organik terbaik. Pelaksanaan penelitian berada di Green House Universitas Nusa Bangsa, Bogor. Waktu penelitian di bulan April sampai dengan Juni 2020. Metode pada kajian menggunakan metode penelitian eksperimental, dengan tujuh perlakuan yang dirancang secara acak lengkap (RAL). Perlakuan yang dicobakan adalah: 1) P0: tanah (kontrol), 2) P1: tanah dan kompos perbandingan volume 1:1, 3) P2: tanah dan arang kulit padi perbandingan volume 1:1, 4) P3: tanah dan rabuk kandang kotoran kambing perpaduan isi 1:1, 5) P4: tanah, kompos dan arang kulit padi dengan perpaduan volume 1:1:1, 6) P5: tanah, humus, dan rabuk kandang kotoran kambing perbandingan volume 1:1:1, dan 7) P6: tanah, kompos, arang kulit padi dan rabuk kandang kotoran kambing volume perpaduan 1:1:1:1. Percobaan diulang 3 kali untuk setiap unit. Hasil kajian menunjukkan bahwa kombinasi material organik memberikan respon berbeda terhadap kemajuan dan hasil tanaman pakcoy (Brassica rapa L.). Pola pertumbuhan (tinggi tanaman dan kuantitas daun) pada P3, P5 dan P6 sama. Perlakuan terbaik adalah P5 (kombinasi tanah, humus, rabuk kandang kotoran kambing dengan pepaduan volume media 1 : 1 : 1 (P5) yang sama nyata dengan perlakuan P3 dan P6. AbstractPlanting media is part of the important factors to determine the development and growth of plants. The quality will determine the productivity of the plant. This study aims to examine the effect of a combination of several organic materials, namely husk charcoal, compost, and goat manure as a planting medium on the growth and yield of pakcoy plants and determine the best combination of organic materials. The research was conducted at the Green House of Nusa Bangsa University, Bogor. The time of the study was from April to June 2020. The method in this study used an experimental research method, with seven treatments designed at completely randomized (CRD). The treatments were: 1) P0: soil (control), 2) P1: soil and compost volume ratio 1:1, 3) P2: soil and rice husk charcoal volume ratio 1:1, 4) P3: soil and manure goat manure a mixture of 1:1 content, 5) P4: soil, compost and rice bran charcoal with a volume combination of 1:1:1, 6) P5: soil, humus, and goat manure ratio 1:1:1, 7) P6: soil, compost, rice husk charcoal and goat manure manure mixed volume 1:1:1:1. The experiment was repeated 3 times for each unit. The results of the study showed that the combination of organic materials gave different responses to the progress and yield of pakcoy (Brassica rapa L.). The growth pattern (plant height and leaf quantity) at P3, P5 and P6 were the same. The best treatment was P5 (a combination of soil, humus, goat manure manure with a mix of 1:1:1 (P5) media volume which was as significant as P3 and P6 treatments.

Euclidean Distance Degree and Mixed Volume

We initiate a study of the Euclidean distance degree in the context of sparse polynomials. Specifically, we consider a hypersurface $$f=0$$ f = 0 defined by a polynomial f that is general given its support, such that the support contains the origin. We show that the Euclidean distance degree of $$f=0$$ f = 0 equals the mixed volume of the Newton polytopes of the associated Lagrange multiplier equations. We discuss the implication of our result for computational complexity and give a formula for the Euclidean distance degree when the Newton polytope is a rectangular parallelepiped.

Using tomography, CFD, and dynamic tests to study the continuous-flow mixing of yield-pseudoplastic fluids

The major technological challenges faced by modern chemical industries are non-ideal flows such as dead zones and channeling encountered in the mixing of fluids with complex rheology. These cause sub-optimal mixing and lead to low quality products and high costs of raw materials. Therefore, the core objectives of this study were to develop methodology and tools to design an efficient continuous-flow mixing system for the fluids with complex rheology using electrical resistance tomography (ERT), computational fluid dynamics (CFD), and dynamic tests. The xanthan gum solution, which is a pesudoplastic fluid with yield stress, was used to study the dynamic behavior of the continuous-flow mixing process. The power consumption, cavern size, mixing time, and the extents of channelling and the fraction of fully mixed volume were successfully determined using dynamic tests, ERT tests, and CFD simulations and used as mixing quality criteria. A novel and efficient method was developed for flow visualization in the continuous-flow mixing of opaque fluids using 2D and 3D tomograms. A unique study on identifying the sources of flow non-ideality in non-Newtonian fluids with yield stress was done by visualizing the flow pattern inside the continuous-flow mixing vessel using 2D and 3D tomograms. The deformation of the cavern was analyzed and quantified in the continuous-flow mixing system for yield-pseudoplastic fluids using ERT. Moreover, the cavern volume was compared with the fully mixed volume and it was found that the latter was higher due to the extra momentum induced by the inlet-outlet flow. A novel study on exploring the effect of the rheological parameters of the pseudoplastic fluids with yield stress on the non ideal flows in a continuous-flow mixing system was performed using CFD. The CFD results revealed that the mixing quality was improved when the degree of the shear thinning was increased. The ratio of the residence time to the batch mixing time was evaluated to achieve ideal mixing for the continuous-flow mixing of yield-pseudoplastic fluids using dynamic tests and ERT. It was found that the ratio of residence time to the batch mixing time should be at least 8.2 or higher to achieve ideal mixing.

Dynamic & CFD modeling of a continuous-flow mixer using fluids with yield stress

A continuous-flow mixer was designed and built in the Mixing Technology Lab, Chemical Engineering Department at Ryerson University to study mixing of xanthan gum solutions in water, a pseudoplastic fluid possessing yield stress. The extent of flow non-ideality was quantified using a dynamic model that incorporated the extent of channeling and the effective mixed volume within the mixing vessel. Dynamic tests were made using a frequency-modulated random binary input of a brine solution. The same experiments were simulated using Fluent, a Computational Fluid Dynamics (CFD) package. CFD flow fields were used to obtain the system dynamic response to a tracer injection applied at conditions indentical to the experimental conditions. The extent of channeling and effective mixed volume were determined and then compared with the parameters obtained experimentally. Experimental and CFD results show that the extent of non-ideal flow is significantly affected by impeller speed, impeller type, feed flow rate, fluid rheology, and exit location. The performance of continuous mixed vessels can be improved by increasing impeller speed, decreasing feed flow rate, and decreasing solution concentration. However, decreasing feed flow rate and solution concentration reduces the production capacity of the process. Increasing impeller speed may require modification to the motor and can cause air entrainment. Therefore, other remedies such as relocating the exit location and using the proper type of impeller may be taken into consideration. The results show that the extent of non-ideal flow was reduced using the bottom output and flow efficiency in the vessel was enhanced using A320 impeller.

Using tomography, CFD, and dynamic tests to study the continuous-flow mixing of yield-pseudoplastic fluids

The major technological challenges faced by modern chemical industries are non-ideal flows such as dead zones and channeling encountered in the mixing of fluids with complex rheology. These cause sub-optimal mixing and lead to low quality products and high costs of raw materials. Therefore, the core objectives of this study were to develop methodology and tools to design an efficient continuous-flow mixing system for the fluids with complex rheology using electrical resistance tomography (ERT), computational fluid dynamics (CFD), and dynamic tests. The xanthan gum solution, which is a pesudoplastic fluid with yield stress, was used to study the dynamic behavior of the continuous-flow mixing process. The power consumption, cavern size, mixing time, and the extents of channelling and the fraction of fully mixed volume were successfully determined using dynamic tests, ERT tests, and CFD simulations and used as mixing quality criteria. A novel and efficient method was developed for flow visualization in the continuous-flow mixing of opaque fluids using 2D and 3D tomograms. A unique study on identifying the sources of flow non-ideality in non-Newtonian fluids with yield stress was done by visualizing the flow pattern inside the continuous-flow mixing vessel using 2D and 3D tomograms. The deformation of the cavern was analyzed and quantified in the continuous-flow mixing system for yield-pseudoplastic fluids using ERT. Moreover, the cavern volume was compared with the fully mixed volume and it was found that the latter was higher due to the extra momentum induced by the inlet-outlet flow. A novel study on exploring the effect of the rheological parameters of the pseudoplastic fluids with yield stress on the non ideal flows in a continuous-flow mixing system was performed using CFD. The CFD results revealed that the mixing quality was improved when the degree of the shear thinning was increased. The ratio of the residence time to the batch mixing time was evaluated to achieve ideal mixing for the continuous-flow mixing of yield-pseudoplastic fluids using dynamic tests and ERT. It was found that the ratio of residence time to the batch mixing time should be at least 8.2 or higher to achieve ideal mixing.