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"There have been many recent and important developments based on effective field theory and the renormalization group in atomic, condensed matter, nuclear and high-energy physics. These powerful and versatile methods provide novel approaches to study complex and strongly interacting many-body systems in a controlled manner. The six extensive lectures gathered in this volume combine selected introductory and interdisciplinary presentations focused on recent applications of effective field theory and the renormalization group to many-body problems in such diverse fields as BEC, DFT, extreme matter, Fermi-liquid theory and gauge theories. "

"The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the field, V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity, R. Seiringer describes a proof of Bose-Einstein condensation in the Gross-Pitaevski limit and explains the effects of rotating traps and the emergence of lattices of quantized vortices, J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to the functional analytic methods used to prove their thermodynamic stability, finally, T. Spencer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures are characterized by their mathematical rigor combined with physical insights."

"The volume presents, for the very first time, an exhaustive collection of those modern theoretical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and materials science, belong to this class of systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. "

"This book collects chapters dealing with some of the theoretical aspects needed to properly discuss the dynamics of complex engineering systems. The book illustrates advanced theoretical development and new techniques designed to better solve problems within the nonlinear dynamical systems. Topics covered in this volume include advances on fixed point results on partial metric spaces, localization of the spectral expansions associated with the partial differential operators, irregularity in graphs and inverse problems, Hyers-Ulam and Hyers-Ulam-Rassias stability for integro-differential equations, fixed point results for mixed multivalued mappings of Feng-Liu type on Mb-metric spaces, and the limit q-Bernstein operators, analytical investigation on the fractional diffusion absorption equation."

"Kami menunjukkan penelitian secara teoretik pada kenaikan nilai magnetisasi dari sistem nanopartikel Fe3O4 dengan adanya penambahan reduced Graphene Oxide (rGO). Data eksperimen telah menunjukkan bahwa magnetisasi sistem nanopartikel Fe3O4 -rGO meningkat dengan peningkatan jumlah rGO sampai sekitar 5 wt%, tetapi menurun kembali dengan bertambah lebih banyaknya jumlah rGO. Kami mengajukkan bahwa kenaikan terjadi dipengaruhi oleh adanya pembalikan spin pada Fe3+ dalam bagian tertrahedral dibantu oleh kekosongan oksigen di perbatasan partikel Fe3O4 . Kekosongan oksigen diinduksi oleh adanya lapisan rGO yang menarik atom oksigen dari permukaan partikel Fe3O4 disekitarnya. Untuk memahami peningkatan mag- netisasi, kami mengkontruksi model Hamiltonian berdasarkan tight-binding untuk sistem nanopartikel Fe3O4 dengan konsentrasi kekosongan oksigen dikontrol melalui konten rGO. Kami menghitung magnetisasi sebagai fungsi dari medan magnet eksternal untuk berbagai variasi wt% rGo. Kami menggunakan metode dynamical mean-field theory dan melakukan perhitungan pada temperatur ruangan. Hasil kami untuk ketergantungan rGO wt% dari magnetisasi saturasi menunjukkan hasil yang sangat sesuai dengan data eksperimen dari sistem nanopartikel Fe3O4 -rGO yang ada. Hasil ini mungkin dapat menkonfirmasi bahwa model kami telah membawa ide paling penting yang dibutuhkan untuk menjelaskan fenomena kenaikan magnetisasi diatas.

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We present a theoretical study on the enhancement of magnetization of Fe3O4 nanoparticle system upon addition of reduced Graphene Oxide (rGO). Experimental data have shown that the magnetization of Fe3O4 -rGO nanoparticle system increases with increasing rGO content up to about 5 wt%, but decreases back as the rGO content increases further. We propose that the enhancement is due to spin-flipping of Fe3+ in the tetrahedral sites assisted by oxygen vacancies at the Fe3O4 particle boundaries. These oxygen vacancies are induced by the presence of rGO flakes that adsorb oxygen atoms from Fe3O4 particles around them. To understand the enhancement of the magnetization we construct a tight-binding based model Hamiltonian for the Fe3O4 nanoparticle system with the concentration of oxygen vacancies being controlled by the rGO content. We calculate the magnetization as a function of the applied magnetic field for various values of rGO wt%. We use the method of dynamical mean-field theory and perform the calculations for a room temperature. Our result for rGO wt% dependence of the saturated magnetization shows a very good agreement with the existing experimental data of the Fe3O4 -rGO nanoparticle system. This result may confirm that our model already carries the most essential idea needed to explain the above phenomenon of magnetization enhancement."