Judul: Dinamika Penyebaran Covid-19 Secara Lokal Berdasarkan Model Ising Multi Keadaan
Abstrak: Model Ising pada umumnya terdiri atas sistem yang di dalamnya terdapat subsistem (spin) yang memiliki satu dari dua keadaan (1 dan −1). Modifikasi model Ising dilakukan dengan menambahkan karakteristik keadaan baru (multi keadaan). Model Ising yang dimodifikasi menjadi lima keadaan (2, 1, 0, −1, dan −2) membuat spin memiliki banyak pilihan apabila terjadi perubahan keadaan. Sehingga dibutuhkan aturan baru dalam metode Monte Carlo untuk mengatur kondisi perubahan spin. Beragam aturan dibuat untuk membatasi banyaknya pilihan dari spin tersebut. Mulai dari pengecekan variasi jumlah rata-rata sekitar hingga pengaruh pemberian faktor eksternal yang dapat menentukan kondisi perubahan spin. Dinamika penyebaran covid-19 secara lokal digunakan sebagai landasan dalam pembuatan aturan tersebut. Hal ini dilakukan agar mudah dalam pengaplikasian dan memperoleh hasil yang diharapkan. Dengan menganggap faktor eksternal sebagai tindakan pemerintah dalam menekan penyebaran covid-19 dan faktor internal sebagai interaksi antar orang. Semakin tinggi pengawasan dari pemerintah, maka banyak orang yang melakukan tindakan untuk mengurangi penyebaran. Akibatnya orang yang terinfeksi menjadi berkurang. Sistem dengan kondisi aturan yang berbeda akan menghasilkan dinamika penyebaran yang berbeda pula. Hasil menunjukkan sistem lebih dipengaruhi faktor eksternal dibandingkan dengan faktor internal. Perbedaan antar jumlah spin memiliki gap yang terlihat jelas dan transisi antar spin menjadi lebih sering terjadi., Ising model generally consist of system which there are subsystem (spins) inside it that can be one of two states (1 and −1). Modification Ising model done by adding new characteristic state (multi-state). Modificated Ising model become five states (2,1,0,−1, and −2) make the spin have a lot of choice, if the spin want to change their states. New rules on Monte Carlo method needed to arrange spin changing condition. Various rules are made to confine spin from many possible choices. From checking variation of surrounding average until the effect of external factor which can determine spin changing condition. The rules was made based on the spread dynamics of covid-19 locally. So its easy to applicate and we can get the desire result. Considering that external factor as a government action and internal factor as people interaction. The more control from government to reducing the spread, more people will take action to reduce the spread. As a result infected people decreased. System with different condition will get different spread dynamics. The results show that external factor more affect the system than internal factor. Different gap between the total of spin clearly seen and the transition between spin occurs more often.
Keyword: dinamika penyebaran, faktor eksternal, metode Monte Carlo, model Ising, external factor, Ising model, Monte Carlo method, the spread dynamics

Judul: Kajian Efek Lockdown dalam Penyebaran Penyakit Menular Covid-19: Analisa Model Matematika SIQ
Abstrak: COVID-19 dapat menyebar dengan cepat melalui kontak langsung dengan penderita COVID-19. Perpindahan penduduk dari wilayah yang telah banyak memiliki kasus COVID-19pun menjadi salah satu penyebab penyakit ini menyebar begitu cepat, maka pembatasan suatu wilayah atau yang biasa disebut dengan lockdown diperlukan untuk dapat menanggulangi penyebaran COVID-19 ini. Model SIQ digunakan untuk mempelajari penyebaran COVID-19. Diperoleh dua titik tetap ketika lockdown diterapkan, yaitu titik tetap bebas penyakit dan titik tetap endemik. Saat titik tetap bebas penyakit, maka penyakit dapat punah. Sedangkan saat titik tetap endemik, berdasarkan simulasi numerik penerapan lockdown berpengaruh untuk menekan peningkatan populasi individu terinfeksi. Pertumbuhan populasi individu terinfeksi saat lockdown juga sangat kecil jika dibandingkan dengan tanpa pemberlakuan lockdown., COVID-19 can spread quickly through direct contact with people with COVID-19. The movement of the people from the areas that already have a lot of COVID-19 cases is also one of the causes of this disease spreading so fast, so the restriction of an area or commonly called a lockdown is needed to be able to cope with the spread of COVID-19. The SIQ model is used to study the spread of COVID-19. Two fixed points are obtained when the lockdown has been implemented, namely the disease-free fixed point and the endemic fixed point. In the disease-free fixed point, the disease can become extinct. Meanwhile, in the endemic fixed point, based on numerical simulations, the implementation of the lockdown is intended to result lower of the level of infected individuals. In fact, the growth of the population of infected individuals when the lockdown is applied is very small, compared to simulation of no lockdown applied.
Keyword: COVID-19, lockdown, mathematical model, SIQ

Judul: Kajian Pemurnian Gliserol Hasil Samping Biodiesel Jarak Pagar Menggunakan Asam Nitrat, Sulfat, dan Fosfat
Abstrak: About ±10% glycerol is produced as byproduct in KOH alkali-catalysis transesterification of Jatropha curcas oil and methanol. The glycerol contains some soluble impurities such as catalyst, soap, excess methanol, water, and other substances. The glycerol needs purification treatment so that glycerol can be utilized into other products. The first step in the glycerol purification is mineral acid addition to neutralize the base content and to split the soap content into salt and free fatty acid that are more easily separated from glycerol. The purposes of this research are to select the kind of acid that could separate the glycerol from the base catalyst and soap, to study the effect of the molar amount of added acid, and to identify the quality of salt as byproduct of glycerol purification with the best treatment. The experiments conducted in complete randomized factorial design, consisted of two treatment factors: kinds and molar amount of mineral acids. Kind of acids were HNO3 15.27 M, H2SO4 18.01 M, and H3PO4 14.74 M. Molar amount of acids were 54 mmol, 90 mmol, 126 mmol, 162 mmol, and 198 mmol (added into 200 g of glycerol). The observed response variables were pH of glycerol, glycerol content, and ash content of glycerol. The crude glycerol from KOH alkali-catalysis of Jatropha curcas biodiesel production contained: glycerol (40.48%), KOH (2.39%), soap (7.82%), evaporated compounds at 1050C (46.81%), and ash (5.16%). The kind and molar amount of mineral acid significantly affected the pH-value, glycerol content, and ash content. The treatment with 126 mmol H3PO4 14.74 M, in 200 grams glycerol, resulted highest glycerol content (78.77%), lowest ash content (1.085%), and pH-value 6.63. Precipitated salt produced from the best treatment contained (based on dry base, except evaporated compounds): K2O (13.17%), P2O5 (20.14%), chloride (2.67%), free acid (26.18%), and evaporated compounds at 1300C (33.93%).
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