Mesoscopic non-equilibrium thermodynamics approach to non-Debye dielectric relaxation

Mesoscopic non-equilibrium thermodynamics is used to formulate a model describing non-homogeneous and non-Debye dielectric relaxation. The model is presented in terms of a Fokker-Planck equation for the probability distribution of non-interacting polar molecules in contact with a heat bath and in the presence of an external time-dependent electric field. Memory effects are introduced in the Fokker-Planck description through integral relations containing memory kernels, which in turn are used to establish a connection with fractional Fokker-Planck descriptions. The model is developed in terms of the evolution equations for the first two moments of the distribution function. These equations are solved by following a perturbative method from which the expressions for the complex susceptibilities are obtained as a functions of the frequency and the wave number. Different memory kernels are considered and used to compare with experiments of dielectric relaxation in glassy systems. For the case of Cole-Cole relaxation, we infer the distribution of relaxation times and its relation with an effective distribution of dipolar moments that can be attributed to different segmental motions of the polymer chains in a melt.Comment: 33 pages, 6 figure

Pattern formation from consistent dynamical closures of uniaxial nematic liquid crystals

Pattern formation in uniaxial polymeric liquid crystals is studied for different dynamic closure approximations. Using the principles of mesoscopic non-equilibrium thermodynamics in a mean-field approach, we derive a Fokker-Planck equation for the single-particle non-homogeneous distribution function of particle orientations and the evolution equations for the second and fourth order orientational tensor parameters. Afterwards, two dynamic closure approximations are discussed, one of them considering the relaxation of the fourth order orientational parameter and leading to a novel expression for the free-energy like function in terms of the scalar order parameter. Considering the evolution equation of the density of the system and values of the interaction parameter for which isotropic and nematic phases coexist, our analysis predicts that patterns and traveling waves can be produced in lyotropic uniaxial nematics even in the absence of external driving.Comment: 34 pages, 7 figure

Spontaneous Fluctuations in Mesoscopic Simulations of Nematic Liquid Crystals

We analyzed hydrodynamic fluctuations in nematic liquid crystals simulated by Multi-particle Collision Dynamics. Velocity effects on orientation were incorporated by allowing mesoscopic velocity gradients to exert torques on nematic particles. Backflow was included through an explicit application of angular momentum conservation during the collision events. We measured the spectra of hydrodynamic fluctuations and compared them with those derived from a linearized hydrodynamic scheme. Numerical results were found to reproduce the expected coupling between hydrodynamic modes, thus showing that the implementation simulates proper nematodynamic effects at the mesoscopic level

Integrating Simulation-Based Optimization for Lean Logistics: A Case Study

The present work aims at the comprehensive application of stochastic and optimization tools with the support of Information and Communication Technologies (ICT) through a case study in a logistics process for electronic goods; simulation and Response Surface Methodology (RSM) are applied for this purpose. The problem to be evaluated is to define an optimal distribution cost for products shipped to wholesale customers located in different cities in Mexico from a manufacturing plant in Tijuana, Mexico. The factors under study are the product allocation for each distribution center, finished good inventory level and on time deliveries, which are supposed to be significant to get the objective. The methodology applied for this problem considers the design of a discrete event simulation model to represent virtually the real life of logistics process, which is considered a complex system due to different activities are interrelated to carry it out. This model is used to execute the different experiments proposed by the RSM. The results obtained from simulation model were analyzed with the RSM to define the mathematical model that allows identifying the parameters of the factors in order to optimize the process. The findings prove how the ICT facilitate the application of stochastic tools with the purpose of process optimization