Classical Liquids in Fractal Dimension

We introduce fractal liquids by generalizing classical liquids of integer dimensions $d = 1, 2, 3$ to a fractal dimension $d_f$. The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same non-integer dimension. Realizations of our generic model system include microphase separated binary liquids in porous media, and highly branched liquid droplets confined to a fractal polymer backbone in a gel. Here we study the thermodynamics and pair correlations of fractal liquids by computer simulation and semi-analytical statistical mechanics. Our results are based on a model where fractal hard spheres move on a near-critical percolating lattice cluster. The predictions of the fractal Percus-Yevick liquid integral equation compare well with our simulation results.Comment: Changed titl

Nematic liquid crystals on curved surfaces - a thin film limit

We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. Main properties of the thin film model, like uniaxiality and parameter phase space, are preserved in the limiting process. For the derived surface Landau-de Gennes model, we consider an L2-gradient flow. The resulting tensor-valued surface partial differential equation is numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties.Comment: 20 pages, 4 figure

Quasiparticle Dynamics in the Kondo Lattice Model at Half Filling

We study spectral properties of quasiparticles in the Kondo lattice model in one and two dimensions including the coherent quasiparticle dispersions, their spectral weights and the full two-quasiparticle spectrum using a cluster expansion scheme. We investigate the evolution of the quasiparticle band as antiferromagnetic correlations are enhanced towards the RKKY limit of the model. In both the 1D and the 2D model we find that a repulsive interaction between quasiparticles results in a distinct antibound state above the two-quasiparticle continuum. The repulsive interaction is correlated with the emerging antiferromagnetic correlations and can therefore be associated with spin fluctuations. On the square lattice, the antibound state has an extended s-wave symmetry.Comment: 8 pages, 11 figure

Проблема утилизации и вторичной переработки пластиковых бутылок

Происходящие глобальные изменения преобразовывают обычную сырьевую экономику в высокотехнологичную, позволяющую рационально использовать имеющиеся ресурсы и при этом не загрязнять окружающую нас среду. Переработка ПЭТ-бутылок позволит решить проблему утилизации пластикового мусора и может стать прибыльным бизнесом. Результаты исследования показали, что сырье, полученное в процессе переработки пластиковых бутылок, может быть использовано для изготовления востребованной продукции.The ongoing global changes transform the conventional raw material economy into a high-tech one, allowing rational use of available resources and at the same time to not polluting the environment around us. Recycling of PET bottles will solve the problem of recycling plastic trash and can become a profitable business. The results of the research showed that secondary raw material, obtained during the processing of plastic bottles can be used for the production of the demanded products

Fractal Liquids

We introduce fractal liquids by generalizing classical liquids of integer dimensions d=1,2,3 to a fractal dimension df. The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same non-integer dimension. Realizations of our generic model system include microphase separated binary liquids in porous media, and highly branched liquid droplets confined to a fractal polymer backbone in a gel. Here we study the thermodynamics and pair correlations of fractal liquids by computer simulation and semi-analytical statistical mechanics. Our results are based on a model where fractal hard spheres move on a near-critical percolating lattice cluster. The predictions of the fractal Percus-Yevick liquid integral equation compare well with our simulation results

A Resolved Simulation Approach to Investigate the Separation Behavior in Solid Bowl Centrifuges Using Material Functions

The separation of finely dispersed particles from liquids is a basic operation in mechanical process engineering. On an industrial scale, continuously operating decanter centrifuges are often used, whose separation principle is based on the density difference between the solid and the liquid phase due to high g-forces acting on both phases. The design of centrifuges is based on the experience on the individual manufacturer or simplified black box models, which only consider a stationary state. Neither the physical behavior of the separation process nor the sediment formation and its transport is considered. In this work, a computationally-efficient approach is proposed to simulate the separation process in decanter centrifuges. Thereby, the open-source computation software OpenFOAM was used to simulate the multiphase flow within the centrifuge. Sedimentation, consolidation of the sediment, and its transport are described by material functions which are derived from experiments. The interactions between the particles and the fluid are considered by locally defined viscosity functions. This work shows that the simulation method is suitable for describing the solid-liquid separation in a simplified test geometry of a decanter centrifuge. In addition, the influence of the rheological behavior on the flow in the test geometry can be observed for the first time