Rotational Perturbations of Friedmann-Robertson-Walker Type Brane-World Cosmological Models

First order rotational perturbations of the Friedmann-Robertson-Walker metric are considered in the framework of the brane-world cosmological models. A rotation equation, relating the perturbations of the metric tensor to the angular velocity of the matter on the brane is derived under the assumption of slow rotation. The mathematical structure of the rotation equation imposes strong restrictions on the temporal and spatial dependence of the brane matter angular velocity. The study of the integrable cases of the rotation equation leads to three distinct models, which are considered in detail. As a general result we find that, similarly to the general relativistic case, the rotational perturbations decay due to the expansion of the matter on the brane. One of the obtained consistency conditions leads to a particular, purely inflationary brane-world cosmological model, with the cosmological fluid obeying a non-linear barotropic equation of state.Comment: 14 pages, 5 figures, REVTEX

Queueing Network Models for Parallel Processing of Task Systems: an Operational Approach

Computer performance modeling of possibly complex computations running on highly concurrent systems is considered. Earlier works in this area either dealt with a very simple program structure or resulted in methods with exponential complexity. An efficient procedure is developed to compute the performance measures for series-parallel-reducible task systems using queueing network models. The procedure is based on the concept of hierarchical decomposition and a new operational approach. Numerical results for three test cases are presented and compared to those of simulations

Efficient Dynamic Compressor Optimization in Natural Gas Transmission Systems

The growing reliance of electric power systems on gas-fired generation to balance intermittent sources of renewable energy has increased the variation and volume of flows through natural gas transmission pipelines. Adapting pipeline operations to maintain efficiency and security under these new conditions requires optimization methods that account for transients and that can quickly compute solutions in reaction to generator re-dispatch. This paper presents an efficient scheme to minimize compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flow. The optimization scheme relies on a compact representation of gas flow physics, a trapezoidal discretization in time and space, and a two-stage approach to minimize energy costs and maximize smoothness. The resulting large-scale nonlinear programs are solved using a modern interior-point method. The proposed optimization scheme is validated against an integration of dynamic equations with adaptive time-stepping, as well as a recently proposed state-of-the-art optimal control method. The comparison shows that the solutions are feasible for the continuous problem and also practical from an operational standpoint. The results also indicate that our scheme provides at least an order of magnitude reduction in computation time relative to the state-of-the-art and scales to large gas transmission networks with more than 6000 kilometers of total pipeline

Causal Bulk Viscous Dissipative Isotropic Cosmologies with Variable Gravitational and Cosmological Constants

We consider the evolution of a flat Friedmann-Robertson-Walker Universe, filled with a causal bulk viscous cosmological fluid, in the presence of variable gravitational and cosmological constants. The basic equation for the Hubble parameter, generalizing the evolution equation in the case of constant gravitational coupling and cosmological term, is derived, under the supplementary assumption that the total energy of the Universe is conserved. By assuming that the cosmological constant is proportional to the square of the Hubble parameter and a power law dependence of the bulk viscosity coefficient, temperature and relaxation time on the energy density of the cosmological fluid, two classes of exact solutions of the field equations are obtained. In the first class of solutions the Universe ends in an inflationary era, while in the second class of solutions the expansion of the Universe is non-inflationary for all times. In both models the cosmological "constant" is a decreasing function of time, while the gravitational "constant" increases in the early period of evolution of the Universe, tending in the large time limit to a constant value.Comment: 14 pages, 15 figure

Distinguishing impurity concentrations in GaAs and AlGaAs, using very shallow undoped heterostructures

We demonstrate a method of making a very shallow, gateable, undoped 2-dimensional electron gas. We have developed a method of making very low resistivity contacts to these structures and systematically studied the evolution of the mobility as a function of the depth of the 2DEG (from 300nm to 30nm). We demonstrate a way of extracting quantitative information about the background impurity concentration in GaAs and AlGaAs, the interface roughness and the charge in the surface states from the data. This information is very useful from the perspective of molecular beam epitaxy (MBE) growth. It is difficult to fabricate such shallow high-mobility 2DEGs using modulation doping due to the need to have a large enough spacer layer to reduce scattering and switching noise from remote ionsied dopants.Comment: 4 pages, 5 eps figure

Viscous Bianchi type I universes in brane cosmology

We consider the dynamics of a viscous cosmological fluid in the generalized Randall-Sundrum model for an anisotropic, Bianchi type I brane. To describe the dissipative effects we use the Israel-Hiscock-Stewart full causal thermodynamic theory. By assuming that the matter on the brane obeys a linear barotropic equation of state, and the bulk viscous pressure has a power law dependence on the energy density, the general solution of the field equations can be obtained in an exact parametric form. The obtained solutions describe generally a non-inflationary brane world. In the large time limit the brane Universe isotropizes, ending in an isotropic and homogeneous state. The evolution of the temperature and of the comoving entropy of the Universe is also considered, and it is shown that due to the viscous dissipative processes a large amount of entropy is created in the early stages of evolution of the brane world.Comment: 13 pages, 5 figures, to appear in Class. Quantum Gra

Renormalization Group Approach to Causal Viscous Cosmological Models

The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type Universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the scaling properties of the gravitational field equations, of the causal evolution equation of the bulk viscous pressure and of the equations of state. The requirement of scale invariance imposes strong constraints on the temporal evolution of the bulk viscosity coefficient, temperature and relaxation time, thus leading to the possibility of obtaining the bulk viscosity coefficient-energy density dependence. For a cosmological model with bulk viscosity coefficient proportional to the Hubble parameter, we perform the analysis of the renormalization group flow around the scale invariant fixed point, therefore obtaining the long time behavior of the scale factor.Comment: 19 pages. RevTeX4. Revised version. Accepted in Classical and Quantum Gravit

Load Embeddings for Scalable AC-OPF Learning

AC Optimal Power Flow (AC-OPF) is a fundamental building block in power system optimization. It is often solved repeatedly, especially in regions with large penetration of renewable generation, to avoid violating operational limits. Recent work has shown that deep learning can be effective in providing highly accurate approximations of AC-OPF. However, deep learning approaches may suffer from scalability issues, especially when applied to large realistic grids. This paper addresses these scalability limitations and proposes a load embedding scheme using a 3-step approach. The first step formulates the load embedding problem as a bilevel optimization model that can be solved using a penalty method. The second step learns the encoding optimization to quickly produce load embeddings for new OPF instances. The third step is a deep learning model that uses load embeddings to produce accurate AC-OPF approximations. The approach is evaluated experimentally on large-scale test cases from the NESTA library. The results demonstrate that the proposed approach produces an order of magnitude improvements in training convergence and prediction accuracy