Large-scale Limit Research Articles

Wind speed reductions by large-scale wind turbine deployments lower turbine efficiencies and set low generation limits

Wind turbines generate electricity by removing kinetic energy from the atmosphere. Large numbers of wind turbines are likely to reduce wind speeds, which lowers estimates of electricity generation from what would be presumed from unaffected conditions. Here, we test how well wind power limits that account for this effect can be estimated without explicitly simulating atmospheric dynamics. We first use simulations with an atmospheric general circulation model (GCM) that explicitly simulates the effects of wind turbines to derive wind power limits (GCM estimate), and compare them to a simple approach derived from the climatological conditions without turbines [vertical kinetic energy (VKE) estimate]. On land, we find strong agreement between the VKE and GCM estimates with respect to electricity generation rates (0.32 and 0.37 We m-2) and wind speed reductions by 42 and 44%. Over ocean, the GCM estimate is about twice the VKE estimate (0.59 and 0.29 We m-2) and yet with comparable wind speed reductions (50 and 42%). We then show that this bias can be corrected by modifying the downward momentum flux to the surface. Thus, large-scale limits to wind power use can be derived from climatological conditions without explicitly simulating atmospheric dynamics. Consistent with the GCM simulations, the approach estimates that only comparatively few land areas are suitable to generate more than 1 We m-2 of electricity and that larger deployment scales are likely to reduce the expected electricity generation rate of each turbine. We conclude that these atmospheric effects are relevant for planning the future expansion of wind power.

A polytree-based adaptive approach to limit analysis of cracked structures

We in this paper present a novel adaptive finite element scheme for limit analysis of cracked structures. The key idea is to develop a general refinement algorithm based on a so-called polytree mesh structure. The method is well suited for arbitrary polygonal elements and furthermore traditional triangular and quadrilateral ones, which are considered as special cases. Also, polytree meshes are conforming and can be regarded as a generalization of quadtree meshes. For the aim of this paper, we restrict our main interest in plane-strain limit analysis to von Mises-type materials, yet its extension to a wide class of other solid mechanics problems and materials is completely possible. To avoid volumetric locking, we propose an approximate velocity field enriched with bubble functions using Wachspress coordinates on a primal-mesh and design carefully strain rates on a dual-mesh level. An adaptive mesh refinement process is guided by an L2-norm-based indicator of strain rates. Through numerical validations, we show that the present method reaches high accuracy with low computational cost. This allows us to perform large-scale limit analysis problems favorably.

Large-scale Service Systems with Packing Constraints and Heterogeneous Servers

A service system with multiple types of arriving customers and multiple types of servers is considered. Several customers (possibly of different types) can be placed for concurrent service into same server, subject to "packing" constraints, which depend on the server type. Service times of different customers are independent, even if served simultaneously by the same server. The largescale asymptotic regime is considered such that the customer arrival rates grow to infinity. We consider two variants of the model. For the infinite-server model, we prove asymptotic optimality of the Greedy Random (GRAND) algorithm in the sense of minimizing the weighted (by type) number of occupied servers in steadystate. (This version of GRAND generalizes that introduced in [1] for the homogeneous systems, with all servers of same type.) We then introduce a natural extension of GRAND algorithm for finite-server systems with blocking. Assuming subcritical system load, we prove existence, uniqueness, and local stability of the large-scale system equilibrium point such that no blocking occurs. This result strongly suggests a conjecture that the steady-state blocking probability under the algorithm vanishes in the large-scale limit.

Correlation structure of the corrector in stochastic homogenization

Recently, the quantification of errors in the stochastic homogenization of divergence-form operators has witnessed important progress. Our aim now is to go beyond error bounds, and give precise descriptions of the effect of the randomness, in the large-scale limit. This paper is a first step in this direction. Our main result is to identify the correlation structure of the corrector, in dimension $3$ and higher. This correlation structure is similar to, but different from that of a Gaussian free field.

Large-scale drift and Rossby wave turbulence

We study drift/Rossby wave turbulence described by the large-scale limit of the Charney–Hasegawa–Mima equation. We define the zonal and meridional regions as and respectively, where is in a plane perpendicular to the magnetic field such that kx is along the isopycnals and ky is along the plasma density gradient. We prove that the only types of resonant triads allowed are and . Therefore, if the spectrum of weak large-scale drift/Rossby turbulence is initially in Z it will remain in Z indefinitely. We present a generalised Fjørtoft’s argument to find transfer directions for the quadratic invariants in the two-dimensional -space. Using direct numerical simulations, we test and confirm our theoretical predictions for weak large-scale drift/Rossby turbulence, and establish qualitative differences with cases when turbulence is strong. We demonstrate that the qualitative features of the large-scale limit survive when the typical turbulent scale is only moderately greater than the Larmor/Rossby radius.

Characterization of laser-produced carbon plasmas relevant to laboratory astrophysics

Experiments, analytic modeling, and numerical simulations are presented to characterize carbon plasmas produced by high-intensity (109−1013 W cm−2) lasers relevant to experimental laboratory astrophysics. In the large-scale limit, the results agree well with a self-similar isentropic, adiabatic fluid model. Laser-target simulations, however, show small-scale structure in the velocity distribution of different ion species, which is also seen in experiments. These distributions indicate that most of the plasma energy resides in moderate charge states (C+3–C+4), most of the mass resides in the lowest charge states, and the highest charge states move fastest.

A renormalization scheme and skewness of height fluctuations in (1 + 1)-dimensional VLDS dynamics

We study the (1 + 1)-dimensional Villain, Lai, and Das Sarma (VLDS) equation driven by a Gaussian white noise and implement a renormalization scheme without rescaling at one-loop order. Using a diagrammatic method, we calculate the renormalized second and third moments in the large-scale and long-time limits. The ensuing skewness value is S = −0.0441. This (negative) value is consistent with the numerical prediction of Das Sarma et al (1996 Phys. Rev. E 53 359).

Relativistic effects and primordial non-Gaussianity in the matter density fluctuation

We present the third-order analytic solution of the matter density fluctuation in the proper-time hypersurface of nonrelativistic matter flows by solving the nonlinear general relativistic equations. The proper-time hypersurface provides a coordinate system that a local observer can set up without knowledge beyond its neighborhood, along with physical connections to the local Newtonian descriptions in the relativistic context. The initial condition of our analytic solution is set up by the curvature perturbation in the comoving gauge, clarifying its impact on the nonlinear evolution. We compute the effective non-Gaussian parameters due to the nonlinearity in the relativistic equations. With proper coordinate rescaling, we show that the equivalence principle is respected and the relativistic effect vanishes in the large-scale limit.

Peak exclusion, stochasticity and convergence of perturbative bias expansions in 1+1 gravity

The Lagrangian peaks of a 1D cosmological random field representing dark matter are used as a proxy for a catalogue of biased tracers in order to investigate the small-scale exclusion in the two-halo term. The two-point correlation function of peaks of a given height is numerically estimated and analytical approximations that are valid inside the exclusion zone are derived. The resulting power spectrum of these tracers is investigated and shows clear deviations from Poisson noise at low frequencies. On large scales, the convergence of a perturbative bias expansion is discussed. Finally, we go beyond Gaussian statistics for the initial conditions and investigate the subsequent evolution of the two-point clustering of peaks through their Zel'dovich ballistic displacement, to clarify how exclusion effects mix up with scale-dependencies induced by nonlinear gravitational evolution. While the expected large-scale separation limit is recovered, significant deviations are found in the exclusion zone that tends in particular to be reduced at later times. Even though these findings apply to the clustering of one-dimensional tracers, they provide useful insights into halo exclusion and its impact on the two-halo term.

What does convergent evolution mean? The interpretation of convergence and its implications in the search for limits to evolution.

Convergent evolution is central to the study of life's evolutionary history. Researchers have documented the ubiquity of convergence and have used this ubiquity to make inferences about the nature of limits on evolution. However, these inferences are compromised by unrecognized inconsistencies in the definitions, measures, significance tests and inferred causes of convergent evolution. I review these inconsistencies and provide recommendations for standardizing studies of convergence. A fundamental dichotomy exists between definitions that describe convergence as a pattern and those that describe it as a pattern caused by a particular process. When this distinction is not acknowledged it becomes easy to assume that a pattern of convergence indicates that a particular process has been active, leading researchers away from alternative explanations. Convergence is not necessarily caused by limits to evolution, either adaptation or constraint; even substantial amounts of convergent evolution can be generated by a purely stochastic process. In the absence of null models, long lists of examples of convergent events do not necessarily indicate that convergence or any evolutionary process is ubiquitous throughout the history of life. Pattern-based definitions of convergence, coupled with quantitative measures and null models, must be applied before drawing inferences regarding large-scale limits to evolution.

Consistent modified gravity analysis of anisotropic galaxy clustering using BOSS DR11

We analyse the clustering of cosmic large scale structure using a consistent modified gravity perturbation theory, accounting for anisotropic effects along and transverse to the line of sight. The growth factor has a particular scale dependence in f(R) gravity and we fit for the shape parameter f_{R0} simultaneously with the distance and the large scale (general relativity) limit of the growth function. Using more than 690,000 galaxies in the Baryon Oscillation Spectroscopy Survey Data Release 11, we find no evidence for extra scale dependence, with the 95\% confidence upper limit |f_{R0}| <8 \times 10^{-4}. Future clustering data, such as from the Dark Energy Spectroscopic Instrument, can use this consistent methodology to impose tighter constraints.

The MICE Grand Challenge lightcone simulation – II. Halo and galaxy catalogues

This is the second in a series of three papers in which we present an end-to-end simulation from the MICE collaboration, the MICE Grand Challenge (MICE-GC) run. The N-body contains about 70 billion dark-matter particles in a $(3 \, h^{-1} \, {\rm Gpc})^3$ comoving volume spanning 5 orders of magnitude in dynamical range. Here we introduce the halo and galaxy catalogues built upon it, both in a wide ($5000 \,{\rm deg}^2$) and deep ($z<1.4$) light-cone and in several comoving snapshots. Halos were resolved down to few $10^{11} \,h^{-1}\,{\rm M_{\odot}}$. This allowed us to model galaxies down to absolute magnitude M$_r<-18.9$. We used a new hybrid Halo Occupation Distribution and Abundance Matching technique for galaxy assignment. The catalogue includes the Spectral Energy Distributions of all galaxies. We describe a variety of halo and galaxy clustering applications. We discuss how mass resolution effects can bias the large scale $2$-pt clustering amplitude of poorly resolved halos at the $\lesssim 5\%$ level, and their $3$-pt correlation function. We find a characteristic scale dependent bias of $\lesssim 6\%$ across the BAO feature for halos well above $M_{\star}\sim 10^{12}\,h^{-1}\,{\rm M_{\odot}}$ and for LRG like galaxies. For halos well below $M_{\star}$ the scale dependence at $100\,{\rm Mpc} h^{-1}$ is $\lesssim 2\%$. Lastly we discuss the validity of the large-scale Kaiser limit across redshift and departures from it towards nonlinear scales. We make the current version of the light-cone halo and galaxy catalogue (MICECATv1.0) publicly available through a dedicated web portal, http://cosmohub.pic.es, to help develop and exploit the new generation of astronomical surveys.

Exploring the prospects of thermoelectric power generation in conjunction with a water heating system

Thermoelectric generators have long been recognized as a unique energy conversion device due to their capability to convert heat directly into electricity with no moving parts. Nevertheless, engineering applications of these solid-state devices, apart from specialised situations, have been limited by the relatively low intrinsic conversion efficiency of the thermoelectric materials. Many efforts have been made over recent years to improve the conversion efficiency of thermoelectric materials by increasing their figure-of-merit, with only marginal success. The authors recently introduced a novel combination of thermoelectric generators and liquid heaters to carry our two tasks in a manner that compensates for the low efficiency drawback of thermoelectric generators. The idea is to operate the thermoelectric generator in a symbiotic arrangement (a certain configuration of a combined heat and power generation mode – cogeneration) which consists of a stacked assembly of several thermoelectric modules sandwiched between cold and hot liquid passages appropriately connected to an ordinary liquid (e.g. water) heater. It was shown that the system can produce heat and electricity with nearly zero heat dissipation to the surroundings by re-using rejected heat from thermoelectric modules for inlet liquid preheating.In the present research, we aimed to extend our previous study and analyse the large-scale application of this kind of cogeneration system, including considerations of usefulness of this system in such large-scale applications and limitations of this cogeneration system. A theoretical estimation of the maximum achievable electrical power using this symbiotic system has been also presented.

Non-linear curvature inhomogeneities and backreaction for relativistic viscous fluids

The non-perturbative curvature inhomogeneities induced by relativistic viscous fluids are not conserved in the large-scale limit. However, when the bulk viscosity is a function of the total energy density of the plasma (or of the trace of the extrinsic curvature), the relevant evolution equations develop a further symmetry preventing the nonlinear growth of curvature perturbations. In this situation the fully inhomogeneous evolution can be solved to leading order in the gradient expansion. Over large scales, both the acceleration and the curvature inhomogeneities are determined by the bulk viscosity coefficients. Conversely the shear viscosity does not affect the evolution of the curvature and does not produce any acceleration. The curvature modes analyzed here do not depend on the choice of time hypersurfaces and are invariant for infinitesimal coordinate transformations in the perturbative regime.

Vertical upward intermediate scale Taylor flow: Experiments and kinematic closure

The vertical upward Taylor flow regime has been extensively studied at the capillary and large channel scale limits. However, flow behavior at the intermediate scale (5≲Bo≲40, or 6mm≲D≲17mm for ambient gas–water flows) is comparatively poorly characterized. This regime is fundamentally different because classes of forces conventionally associated with either small or large Bond number flows are all relevant. In this investigation, air–water Taylor-flow experiments are conducted in 6.0, 8.0, and 9.5mm diameter tubes. High-speed video data are collected, and automated image analysis algorithms are developed to measure flow parameters including: bubble rise velocity, liquid film thickness, void fraction, and Taylor bubble and liquid slug lengths. New correlations and flow models are developed to predict these parameters at the intermediate scale. Results from this study enable kinematic closure of intermediate scale Taylor flows.

Semi-Markov Model for Market Microstructure

We introduce a new model based on Markov renewal processes (MRP) describing the fluctuations of a tick-by-tick single asset price. We consider a point process associated to the timestamps of the price jumps, with marks associated to price increments. By modelling the marks with a suitable Markov chain, we can reproduce the strong mean-reversion of price returns, a phenomenon known as microstructure noise. Moreover, using MRP, we can model the alternating of time intervals with high and low market activity, and consider dependence between price increments and jump times. We also provide simple parametric and nonparametric statistical procedures for the estimation of our model. We obtain closed-form formula for the mean signature plot, and show the diffusive behaviour of our model at large-scale limit. We illustrate our results by numerical simulations, and find that our model is consistent with available empirical data.

Kurtosis of height fluctuations in (1 + 1) dimensional KPZ dynamics

We study the fourth order normalized cumulant of height fluctuations governed by 1 + 1 dimensional Kardar–Parisi–Zhang (KPZ) equation for a growing surface. Following a diagrammatic renormalization scheme, we evaluate the kurtosis Q from the connected diagrams leading to the value Q = 0.1523 in the large-scale long-time limit.

Large Scale Cloudlets Deployment for Efficient Mobile Cloud Computing

Interest in using Mobile Cloud Computing (MCC) for compute intensive mobile devices jobs such as multimedia applications has been growing. In fact, many new research efforts were invested to maximize the mobile intensive jobs offloading to the cloud within the cloud system coverage area. However, a large scale MCC deployment challenges and limitations are not considered. In this paper, a large scale Cloudlet-based MCC system deployment is introduced, aiming at reducing the power consumption and the network delay of multimedia applications while using MCC. The proposed deployment offers a large coverage area that can be used by mobile devices while they are moving from one location to another to reduce broadband communication needs. Practical experimental results and simulated results using show that using the proposed model reduces the power consumption of the mobile devices as well as reducing the communication latency when the mobile device requests a job to be performed remotely while satisfying the high quality of service requirements of mobile users.

What is the optimal speed limit on freeways?

When choosing his speed, a driver faces a trade-off between private benefits (time savings) and private costs (fuel cost and own damage and injury). Driving faster also has external costs (pollution, adverse health impacts and injury to other drivers). This paper uses large-scale speed limit increases in the western United States in 1987 and 1996 to address three related questions. First, do the social benefits of raising speed limits exceed the social costs? Second, do the private benefits of driving faster exceed the private costs? Third, what is the optimal speed limit? I find that a 10mph speed limit increase on highways leads to a 3–4mph increase in travel speed, 9–15% more accidents, 34–60% more fatal accidents, and elevated pollutant concentrations of 14–24% (carbon monoxide), 8–15% (nitrogen oxides), 1–11% (ozone) and 9% higher fetal death rates around the affected freeways. Using these estimates, I find that the social costs of speed limit increases are two to seven times larger than the social benefits. In contrast, many individual drivers would enjoy a net private benefit from driving faster. Privately, a value of a statistical life (VSL) of $6.0 million or less justifies driving faster, but the social planner's VSL could be at most $0.9–$2.0 million to justify higher speed limits. I conclude that the optimal speed limit was lower, but not much lower, than 55mph.

Sampling social networks using shortest paths

In recent years, online social networks (OSN) have emerged as a platform of sharing variety of information about people, and their interests, activities, events and news from real worlds. Due to the large scale and access limitations (e.g., privacy policies) of online social network services such as Facebook and Twitter, it is difficult to access the whole public network in a limited amount of time. For this reason researchers try to study and characterize OSN by taking appropriate and reliable samples from the network. In this paper, we propose to use the concept of shortest path for sampling social networks. The proposed sampling method first finds the shortest paths between several pairs of nodes selected according to some criteria. Then the edges in these shortest paths are ranked according to the number of times that each edge has appeared in the set of found shortest paths. The sampled network is then computed as a subgraph of the social network which contains a percentage of highly ranked edges. In order to investigate the performance of the proposed sampling method, we provide a number of experiments on synthetic and real networks. Experimental results show that the proposed sampling method outperforms the existing method such as random edge sampling, random node sampling, random walk sampling and Metropolis–Hastings random walk sampling in terms of relative error (RE), normalized root mean square error (NMSE), and Kolmogorov–Smirnov (KS) test.