Asymptotic Behavior of Solutions for the Cauchy Problem of a Dissipative Boussinesq-Type Equation

We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time weighted spaces are established by the contraction mapping principle

Holographic Entanglement Entropy for 4D Conformal Gravity

Using the proposal for holographic entanglement entropy in higher derivative gravities, we compute holographic entanglement entropy for the conformal gravity in four dimensions which turns out to be finite. However, if one subtracts the contribution of the four dimensional Gauss-Bonnet term, the corresponding entanglement entropy has a divergent term and indeed restricted to an Einstein solution of the conformal gravity, the resultant entanglement entropy is exactly the same as that in the Einstein gravity. We will also make a comment on the first law of the entanglement thermodynamics for the conformal gravity in four dimensions.Comment: 16 pages, Published Versio

Entanglement Entropy for Logarithmic Conformal Field Theory

We study holographic entanglement entropy for certain logarithmic conformal field theories by making use of their gravity descriptions. The corresponding gravity descriptions are provided by higher derivative gravity at critical points where the equations of motion degenerate leading to a log gravity. When the central charge of the dual theory is zero, the entanglement entropy has a new divergent term whose coefficient is given by the new anomaly of the logarithmic conformal field theory.Comment: 16 pages, no figures, V2: Refs. added, typos fixed, V3: Published versio

Quantum non-Markovianity, quantum coherence and extractable work in a general quantum process

A key concept in quantum thermodynamics is extractable work, which specifies the maximum amount of work that can be extracted from a quantum system. Different quantities are used to measure extractable work, the most prevalent of which are ergotropy and the difference between the non-equilibrium and equilibrium quantum free energy. Using the former, we investigate the evolution of extractable work when an open quantum system goes through a general quantum process described by a completely-positive and trace-preserving dynamical map. We derive a fundamental equation of thermodynamics for such processes as a relation between the distinct sorts of energy change in such a way the first and second laws of thermodynamics are combined. We then identify the contributions made by the reversible and irreversible processes in this equation and demonstrate that they are respectively responsible for the heat flow and change in the extractable work during the process. Furthermore, we discuss the potential benefit of this assignment in favor of a clear explanation of the impact of quantum effects on the evolution of extractable work. Specifically, we establish this by directly connecting the extractable work with standard quantifiers of quantum non-Markovianity and quantum coherence during the process. We illustrate these results with two examples.Comment: 8 pages, 2 figure

Complexity Growth with Lifshitz Scaling and Hyperscaling Violation

Using complexity=action proposal we study the growth rate of holographic complexity for Lifshitz and hyperscaling violating geometries. We will consider both one and two sided black branes in an Einstein-Maxwell-Dilaton gravitational theory. We find that in either case Lloyd's bound is violated and the rate of growth of complexity saturates to a value which is greater than twice the mass of the corresponding black brane. This value reduces to the mass of the black brane in the isotropic case. We show that in two sided black brane the saturation happens from above while for one sided black brane it happens from below.Comment: 17 pages, 4 figures, v2: typos corrected, references added, v3: Minor corrections, New counter terms added that also contribute to the rate of complexity growth. The conclusion is not changed, now 19 pages, v4: matches published versio

A Highly Reliable Propulsion System with Onboard Uninterruptible Power Supply for Train Application:Topology and Control

Providing uninterrupted electricity service aboard the urban trains is of vital importance not only for reliable signaling and accurate traffic management but also for ensuring the safety of passengers and supplying emergency equipment such as lighting and signage systems. Hence, to alleviate power shortages caused by power transmission failures while the uninterruptible power supplies installed in the railway stations are not available, this paper suggests an innovative traction drive topology which is equipped by an onboard hybrid energy storage system for railway vehicles. Besides, to limit currents magnitudes and voltages variations of the feeder during train acceleration and to recuperate braking energy during train deceleration, an energy management strategy is presented. Moreover, a new optimal model predictive method is developed to control the currents of converters and storages as well as the speeds of the two open-end-windings permanent-magnet-synchronous-machines in the intended modular drive, under their constraints. Although to improve control dynamic performance, the control laws are designed as a set of piecewise affine functions from the control signals based on an offline procedure, the controller can still withstand real-time non-measurable disturbances. The effectiveness of proposed multifunctional propulsion topology and the feasibility of the designed controller are demonstrated by simulation and experimental results

Effect of boundary condition applying type on heat transfer modeling via double species Lattice Boltzmann method

The principle objective of the present study is to solve the velocity and temperature fields using two different distribution functions double species thermal lattice Boltzmann method (TLBM). The study is carried out for a wide range of Rayleigh numbers, velocity and temperature distributions as well as Nusselt numbers were obtained for the Rayleigh numbers ranging from 103 to 106 with the Prandtl number around 0.718 for air. In this simulation, the Boussinesq approximation applied to the buoyancy force term. Also we evaluate the order of derivatives' effect on the accuracy of macroscopic values. So, we applied this method for all of boundary condition types same as no slip, constant temperature and adiabatic walls in two different TLBM model and macroscopic states. We showed that boundary condition applying type has not any difference and based on computer code, we can use both of them with minimum term of derivatives. Results are presented in form of streamline and isothermal plots as well as the variation of average Nusselt number at the walls and domain and compared with commercial CFD softwares and other established methods referenced through literature. A good agreement is obtained between the current solution and the previous works and it shows that we can use double species TLBM with minimum terms of derivatives on a macroscopic and TLBM parameters in boundary conditions discretization. Results are in a good independency from the grids and size of mesh. Finally it is showed that we can solve the first rows and corners (the nodes on the body) of grid with macroscopic terms then continue for other lattices with TLBM to improve accuracy and save the time