Fractional Hamiltonian analysis of higher order derivatives systems

The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives.Comment: 13 page

Texture Characterization of Duplex Stainless Steel 2205 Using Neutron Diffraction Method

Duplex stainless steel (DSS) is widely used in chemical processes, petrochemical, oil & gas industries, and nuclear technology due to its excellent mechanical properties and exceptional generalized and localized corrosion resistance. In this study, the crystal structure, material phases, and texture characterization of DSS were carried out using the neutron diffraction method. The characterization results show that the duplex has two phases: α (ferrite) and g (austenite), each with a lattice parameter 2.8736 Angstrom and 3.6076 Angstrom, respectively. The sample symmetrization method from triclinic to orthorhombic are used to analyze pole figures. The crystallite orientation in the α and g phases have the opposite direction. The α phase has a crystallite orientation towards {110} <001> or Goss orientation, and the g phase, crystal orientation towards {100} <001> or the cube orientation. The orientation distribution function shows that the orientation strength of ferrite is much stronger than austenite. The crystallite orientation (texture) obtained by the orientation distribution function analysis follows the crystal structure analysis

Analysis of Crystal Structure of the Welds with Friction-stir Welding Method on the Retreating Side for Bimetallic Disimilar Aa6061-cu Using Neutron Diffraction Techniques

Crystal structure analysis has been performed on bimetallic disimilar Al-Cu. Neutron diffraction analysis shows that Al lattice parameter decrease from 4.09 Å to 4.05 Å while the Cu lattice parameter is relatively constant. This is due to the melting point ofAl is much lower than the melting point of Cu. Physically, during the Friction Stir Welding (FSW) process in the Stir Zone (SZ) or Nuget Welded Zone (NWZ) region, strong deformation occurs at temperatures around 500 oC. This leads to dynamic recrystallization where grains become more refined. At the Thermo Mechanically Affected Zone (TMAZ) region, atomic diffusion occurs due to a combination of strong plastic deformation at high temperatures. And for Heat Affected Zone (HAZ) area there are aluminium even with a very small percentage of weight, this is due to the exposure at a high temperature during the heating FSW process, similar with annnealing-like process, which leads to the dislocation disappears, dissolves and precipitates grain becomes rough when the temperature exceeds 250 oC

Analisis Tekstur Padalasan Stainless Steel 201 dengan Teknik Difraksi

ANALISIS TEKSTUR PADALASAN STAINLESS STEEL 201 DENGAN TEKNIK DIFRAKSI NEUTRON. Baja tahan karat jenis austenitik merupakan baja tahan karat yang banyak dipakai dalam industri, salah satunya adalah industri rumah tangga. Dalam penelitian ini dilakukan karakterisasi Stainless Steel (SS) 201 yang banyak dijual di pasaran. Sebelum dilakukan karakterisasi, plat SS 201 dipotong dengan ukuran 150 mm × 120 mm× 10 mm, kemudian dibuat lubang berbentuk alur pada kedua permukaan, sehingga alur berbentuk X Double V Groove (DVG), selanjutnya alur DVG dilas dengan sistem pengelasan multi pass menggunakan metode pengelasan Metal Inert Gas (MIG). Bahan yang sudah dilas kemudian dikarakterisasi dengan teknik difraksi neutron untuk mendapatkan pola difraksi dan pole figure pada daerah pusat lasan FusionZone (FZ), daerah terpengaruh panas Heat Affected Zone (HAZ) dan daerah logam dasar Base Metal Zone (BMZ). Selanjutnya pole figure dianalisis dengan perangkat lunak Beartex untukmenentukan arah orientasi dan kekuatan tekstur pada ketiga daerah tersebut. Dari penelitian ini dapat disimpulkan bahwa pada daerah pusat lasan butir kristalit terorientasi {110} dengan tipe Brass dengan indeks tekstur sekitar 3,12 m.r.d (multiple random distribution) yang ditunjukkan pada pole figure 200. Untuk daerah HAZ, tekstur paling kuat terorientasi pada {110} atau tipe Goss dengan indeks tekstur 4,8 m.r.d. Pada daerah logamdasar, tekstur secara dominan terorientasi kearah {010} atau tipe Cube dengan indeks tekstur tidak terlalu kuat, sekitar 1,53 m.r.d. Pada daerah pusat lasan, bidang (110) sejajar dengan sumbu normal (ND), dengan arah kristalit sejajar dengan arah pengerolan (RD) [112]. Pada daerah HAZ bidang (110) tersebut mengarah ke arah sumbu pengerolan [001], dengan indeks tekstur 1,5 kali lebih kuat dibanding FZ. Hal ini menunjukkan bahwa bidang (110) yang semula terorientasi kearah [112] pada FZ berubah menjadi sekitar 35,26º ke arah [001] pada daerah HAZ. Untuk daerah logamdasar bidang (010)mengarah sejajar dengan arah normal (ND) dan teksturmengarah pada arah pengerolan (RD) [100]

Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.Comment: 10 page

Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.Comment: 9 page

Solutions of a particle with fractional δ\delta-potential in a fractional dimensional space

A Fourier transformation in a fractional dimensional space of order \la (0<\la\leq 1) is defined to solve the Schr\"odinger equation with Riesz fractional derivatives of order \a. This new method is applied for a particle in a fractional $\delta$-potential well defined by V(x) =- \gamma\delta^{\la}(x), where $\gamma>0$ and \delta^{\la}(x) is the fractional Dirac delta function. A complete solutions for the energy values and the wave functions are obtained in terms of the Fox H-functions. It is demonstrated that the eigen solutions are exist if 0< \la<\a. The results for \la= 1 and \a=2 are in exact agreement with those presented in the standard quantum mechanics

A Scaling Method and its Applications to Problems in Fractional Dimensional Space

A scaling method is proposed to find (1) the volume and the surface area of a generalized hypersphere in a fractional dimensional space and (2) the solid angle at a point for the same space. It is demonstrated that the total dimension of the fractional space can be obtained by summing the dimension of the fractional line element along each axis. The regularization condition is defined for functions depending on more than one variable. This condition is applied (1) to find a closed form expression for the fractional Gaussian integral, (2) to establish a relationship between a fractional dimensional space and a fractional integral, (3) to develop the Bochner theorem, and (4) to obtain an expression for the fractional integral of the Mittag–Leffler function. Some possible extensions of this work are also discussed