Judul: Uji Kinerja Reaktor Biodiesel Berpengaduk Tipe Pedal 45° Pitch Blade Untuk Produksi Biodiesel Berbahan Minyak Jelantah
Abstrak: Biodiesel merupakan salah satu energi alternatif yang dikembangkan oleh pemerintah Indonesia untuk menggantikan solar berbasis minyak bumi. Salah satu bahan baku yang dapat digunakan untuk membuat biodiesel adalah minyak jelantah. Pada proses transesterifikasi pembuatan biodiesel dibutuhkan pencampuran yang kuat, pemilihan jenis pengaduk, kecepatan putar (RPM) dan suhu yang tepat. Pada penelitian ini digunakan reaktor tipe batch dengan pengaduk tipe pedal 45° pitch blade. Penelitian ini bertujuan untuk mengetahui performansi pengaduk yang dipakai dan mengetahui RPM yang tepat untuk menghasilkan biodiesel yang bermutu sesuai standar. Kecepatan putar (RPM) yang digunakan untuk pengujian pembuatan biodiesel adalah 300, 500, dan 1000 dengan suhu sebesar 60 ̊C. Hasil penelitian menunjukkan bahwa sebaran pola aliran dengan menggunakan pengaduk tipe pedal 45° pitch blade menghasilkan aliran radial dan aksial. Berdasarkan uji mutu dan analisis pemilihan biodiesel menggunakan metode pembobotan (scorring), hasil perlakuan terbaik didapatkan pada RPM 500 yang memiliki rendemen biodiesel sebesar 91,76%, densitas 0,835 g/ml, viskositas 4,537 cSt, dan bilangan asam sebesar 0,415 mgKOH / g sampel. Konsumsi energi listrik total proses transesterifikasi adalah sebesar 1,0707 kWh, sedangkan biaya listrik proses transesterifikasi adalah sebesar Rp 1.541,81.
Keyword: biodiesel, minyak jelantah, pengaduk, rpm, transesterifikasi, stirer, transesterification, waste cooking oil

Judul: Performance test of biodiesel reactor using multistage strirrer type
Abstrak: Reaktor biodiesel merupakan salah satu penentu dalam proses memproduksi biodiesel. Agar reaksi dapat terjadi secara sempurna, maka pengadukan menjadi faktor yang sangat penting dalam reaktor biodiesel. Penelitian ini bertujuan untuk menguji performansi reaktor tipe batch dengan berpengaduk turbin bertingkat dengan bahan baku minyak jelantah dan metanol. Pengujian reaktor untuk membuat biodiesel dilakukan pada 5 tingkat kecepatan putar pengaduk, yaitu 50 RPM, 200 RPM, 400 RPM, 500 RPM, dan 900 RPM. Suhu reaksi dipertahankan pada 60°C selama 60 menit. Parameter yang diukur adalah daya motor yang dibutuhkan reaktor dan karateristik biodiesel berupa densitas, gliserol total, bilangan asam, angka penyabunan dan kadar metil ester. Hasil penelitian menunjukkan bahwa perlakuan kecepatan putar 50 RPM dan 900 RPM tidak membentuk biodiesel. Sedangkan pada perlakuan 200 RPM, 400 RPM dan 500 RPM dihasilkan biodiesel dengan karakteristik yang telah memenuhi SNI biodiesel. Perlakuan 200 RPM memiliki rendemen terbesar (88%) dan daya motor terkecil (489 W). Perlakuan 500 RPM menghasilkan kadar metil ester terbesar, yakni 98.9 %, namun memiliki rendemen terkecil (83%) dan daya terbesar (514 W). Berdasarkan hasil tersebut, maka perlakuan 200 RPM direkomendasikan sebagai perlakuan terbaik pada reaktor biodiesel dengan pengaduk tipe turbin bertingkat., The biodiesel reactor is one of the determinants in the process of producing biodiesel. In order for the reaction to occur completely, stirring is a very important factor in a biodiesel reactor. This study aims to test the performance of a batch reactor with a stirred multistage turbine with used cooking oil and methanol as raw materials. Testing of the reactor for making biodiesel was carried out at 5 levels of stirrer rotational speed, namely 50 RPM, 200 RPM, 400 RPM, 500 RPM, and 900 RPM. The reaction temperature was maintained at 60°C for 60 min. The parameters measured were the motor power required by the reactor and the biodiesel characteristics in the form of density, total glycerol, acid number, saponification number and methyl ester content. The results showed that the 50 RPM and 900 RPM rotational speeds did not form biodiesel. While the treatment of 200 RPM, 400 RPM and 500 RPM produced biodiesel with characteristics that have met SNI biodiesel. The 200 RPM treatment had the largest yield (88%) and the smallest motor power (489 W). The 500 RPM treatment produced the highest methyl ester content, which was 98.9%, but had the smallest yield (83%) and the largest power (514 W). Based on these results, the 200 RPM treatment is recommended as the best treatment for a biodiesel reactor with a multistage turbine type stirrer.
Keyword: stirrer, turbine, grade

Judul: The Construction of Greedy SVP LLL Algorithm
Abstrak: A lattice is a set of all integer linear combination of a set of linearly independent vectors in ℝ𝑛���. The independent vectors are called bases of lattice. Any lattice can be generated from many bases, and these bases have the same cardinality. In the lattice, the most fundamental and renowned problem is the Shortest Vector Problem (SVP). SVP is a tracking problem of the shortest nonzero vector in a lattice with equivalent bases. In two dimensions, SVP problem has resolved exactly by Gauss’ algorithm. When the lattice dimension is higher than two, A.K. Lenstra, H.W. Lenstra and L. Lovasz gave a LLL algorithm to compute approximation of nonzero shortest vector in the lattice. Reduced bases solution obtained from LLL algorithm still be an approximation and has polynomial running time of arbitrary dimension which large enough. In 1994, Schnoor and Euchner modified this LLL algorithm as a new variant which later was named deep insertion LLL algorithm. This algorithm is a modified version of the LLL algorithm to the terms of the exchange step to improve the accuracy of output of LLL reduced bases and applying it to the subset sum problem. The purpose of this research are: (1) Reconstruct the LLL algorithm and deep insertion LLL algorithm using a geometric approach. (2) Construct a greedy SVP LLL algorithm. (3) Implement the three algorithms in a symbolic programming language, and evaluate them experimentally. A bases ℬ=[𝐛���1,𝐛���2,…,𝐛���𝑛���] in ℝ𝑚��� is called reduced LLL with parameter 𝛿��� if satisfies: (a) |𝜇���𝑗���𝑖���|≤12, for every integer 𝑖���,𝑗��� with 1≤𝑖���<𝑗���<𝑛���. (b)𝛿���‖𝜋���𝑗���(𝐛���𝑗���)‖2≤‖𝜋���𝑗���(𝐛���𝑗���+1)‖2, for 𝑗���=1,2,…,𝑛���−1,where 𝛿��� is a reduced parameter of real numbers with 14<𝛿���<1. The first requirement is the reduced basis 𝛿��� must “nearly orthogonal” and in its computation case, this requirement can be reached out by using the Gram-Schmidt’s orthogonalization. While the second requirement is called exchange step, or used to called as Lovasz condition. By using both of these requirements, then they establish the LLL algorithm. Then, Schnoor and Euchner modify the LLL algorithm based on the requirements of the exchange step called the deep insertion LLL algorithm, where the exchange step is based on the comparison of the projected vector in orthogonal complement [𝐛���1,𝐛���2,…,𝐛���𝑘���−1]⊥ after j-th reduction. To construct greedy SVP LLL algorithm, the requirements of the exchange step is based on purely by comparing norm of lattice 𝐛���𝑗��� with norm lattice 𝐛���𝑖��� for 𝑖���=1,2,3…,𝑗���−1. The process of insertion reduced vector after the exchange step also has done greedily. Then, we calculate the number of arithmetic operation in greedy SVP LLL algorithm for further analysis. The result of our exprimentation for three algorithms on the certain matrix size shows that the running time of the three algorithms increases propotional to the size of the matrix. The result also shows that by using 𝛿���=34 for the LLL algorithm and the deep insertion LLL algorithm, and the greedy SVP LLL algorithm which is a new variant made by using no parameter of 𝛿���, outperform of the other of two previous algorithm in terms of speed with the same output.
Keyword: LLL algorithm, LLL deep insertion algorithm, greedy SVP LLL algorithm