scholarly journals Fractional relaxation noises, motions and the fractional energy balance equation

2019 ◽  
Author(s):  
Shaun Lovejoy
Keyword(s):  
Energy Balance ◽  
White Noise ◽  
Large Scale ◽  
Energy Balance Equation ◽  
Relaxation Processes ◽  
Relaxation Equation ◽  
Fractional Equations ◽  
Long Memory Process ◽  
Wide Range ◽  
Fractional Relaxation

Abstract. We consider the statistical properties of solutions of the stochastic fractional relaxation equation that has been proposed as a model for the earth's energy balance. In this equation, the (scaling) fractional derivative term models energy storage processes that occur over a wide range of space and time scales. Up until now, stochastic fractional relaxation processes have only been considered with Riemann-Liouville fractional derivatives in the context of random walk processes where it yields highly nonstationary behaviour. For our purposes we require the stationary processes that are the solutions of the Weyl fractional relaxation equations whose domain is −∞ to t rather than 0 to t. We develop a framework for handling fractional equations driven by white noise forcings. To avoid divergences, we follow the approach used in fractional Brownian motion (fBm). The resulting fractional relaxation motions (fRm) and fractional relaxation noises (fRn) generalize the more familiar fBm and fGn (fractional Gaussian noise). We analytically determine both the small and large scale limits and show extensive analytic and numerical results on the autocorrelation functions, Haar fluctuations and spectra. We display sample realizations. Finally, we discuss the prediction of fRn, fRm which – due to long memories is a past value problem, not an initial value problem. We develop an analytic formula for the fRn forecast skill and compare it to fGn. Although the large scale limit is an (unpredictable) white noise that is attained in a slow power law manner, when the temporal resolution of the series is small compared to the relaxation time, fRn can mimick a long memory process with a wide range of exponents ranging from fGn to fBm and beyond. We discuss the implications for monthly, seasonal, annual forecasts of the earth's temperature.

Global and Regional Temperature Projections Using the Fractional Energy Balance Equation

2021 ◽  
Author(s):  
Roman Procyk ◽  
Shaun Lovejoy ◽  
Raphaël Hébert ◽  
Lenin Del Rio Amador
Keyword(s):  
Energy Storage ◽  
Energy Balance ◽  
White Noise ◽  
Climate Sensitivity ◽  
Balance Equation ◽  
Historical Data ◽  
Energy Balance Equation ◽  
Error Model ◽  
Climate Projections ◽  
Equilibrium Climate Sensitivity

<p>We present the Fractional Energy Balance Equation (FEBE): a generalization of the standard EBE.  The key FEBE novelty is the assumption of a hierarchy of energy storage mechanisms: scaling energy storage.  Mathematically the storage term is of fractional rather than integer order.  The special half-order case (HEBE) can be classically derived from the continuum mechanics heat equation used by Budyko and Sellers simply by introducing a vertical coordinate and using the correct conductive-radiative surface boundary conditions (the FEBE is a mild extension).</p><div> <p>We use the FEBE to determine the temperature response to both historical forcings and to future scenarios.  Using historical data, we estimate the 2 FEBE parameters: its scaling exponent (<em>H</em> = 0.38±0.05; <em>H</em> = 1 is the standard EBE) and relaxation time (4.7±2.3 years, comparable to box model relaxation times). We also introduce two forcing parameters: an aerosol re-calibration factor, to account for their large uncertainty, and a volcanic intermittency exponent so that the intermittency volcanic signal can be linearly related to the temperature. The high frequency FEBE regime not only allows for modelling responses to volcanic forcings but also the response to internal white noise forcings: a theoretically motivated error model (approximated by a fractional Gaussian noise). The low frequency part uses historical data and long memory for climate projections, constraining both equilibrium climate sensitivity and historical aerosol forcings. <span>Parameters are estimated in a Bayesian framework using 5 global observational temperature series, and an error model which is a theoretical consequence of the FEBE forced by a Gaussian white noise.</span></p> <p>Using the CMIP5 Representative Concentration Pathways (RCPs) and CMIP6 Shared Socioeconomic Pathways (SSPs) scenario, the FEBE projections to 2100 are shown alongside the CMIP5 MME. The Equilibrium Climate Sensitivity = 2.0±0.4 <sup>o</sup>C/CO<sub>2</sub> doubling implies slightly lower temperature increases.   However, the FEBE’s 90% confidence intervals are about half the CMIP5 size so that the new projections lie within the corresponding CMIP5 MME uncertainties so that both approaches fully agree.   The mutually agreement of qualitatively different approaches, gives strong support to both.  We also compare both generations of General Circulation Models (GCMs) outputs from CMIP5/6 alongside with the projections produced by the FEBE model which are entirely independent from GCMs, contributing to our understanding of forced climate variability in the past, present and future.</p> <p>Following the same methodology, we apply the FEBE to regional scales: estimating model and forcing parameters to produce climate projections at 2.5<sup>o</sup>x2.5<sup>o</sup> resolutions. We compare the spatial patterns of climate sensitivity and projected warming between the FEBE and CMIP5/6 GCMs. </p> </div>

Electron microscopy study of reactively sputter-deposited Ti/N films on silicon

1992 ◽  
Vol 50 (2) ◽  
pp. 1362-1363
Author(s):  
V. C. Kannan ◽  
A. K. Singh ◽  
R. B. Irwin ◽  
S. Chittipeddi ◽  
F. D. Nkansah ◽  
...  
Keyword(s):  
Integrated Circuits ◽  
Large Scale ◽  
Hexagonal Phase ◽  
Microscopy Study ◽  
Electron Microscopy Study ◽  
Process Conditions ◽  
Tin Films ◽  
Wide Range ◽  
Fcc Phase ◽  
Circuits Vlsi

Titanium nitride (TiN) films have historically been used as diffusion barrier between silicon and aluminum, as an adhesion layer for tungsten deposition and as an interconnect material etc. Recently, the role of TiN films as contact barriers in very large scale silicon integrated circuits (VLSI) has been extensively studied. TiN films have resistivities on the order of 20μ Ω-cm which is much lower than that of titanium (nearly 66μ Ω-cm). Deposited TiN films show resistivities which vary from 20 to 100μ Ω-cm depending upon the type of deposition and process conditions. TiNx is known to have a NaCl type crystal structure for a wide range of compositions. Change in color from metallic luster to gold reflects the stabilization of the TiNx (FCC) phase over the close packed Ti(N) hexagonal phase. It was found that TiN (1:1) ideal composition with the FCC (NaCl-type) structure gives the best electrical property.

THE SOME QUESTIONS OF AUTONOMOUS MOTION AND MANAGEMENT OF LAND-MOBILE ROBOTIC COMPLEXES FOR UKRAINIAN GROUND FORCESE

2019 ◽  
pp. 53-58
Author(s):  
О. Кravchuk ◽  
V. Symonenkov ◽  
I. Symonenkova ◽  
O. Hryhorev
Keyword(s):  
Large Scale ◽  
Armed Forces ◽  
Distributed Information ◽  
Wide Range ◽  
Highly Effective ◽  
Information Management Systems ◽  
Robotic Devices ◽  
Principles And Standards ◽  
And Control ◽  
The Eu

Today, more than forty countries of the world are engaged in the development of military-purpose robots. A number of unique mobile robots with a wide range of capabilities are already being used by combat and intelligence units of the Armed forces of the developed world countries to conduct battlefield intelligence and support tactical groups. At present, the issue of using the latest information technology in the field of military robotics is thoroughly investigated, and the creation of highly effective information management systems in the land-mobile robotic complexes has acquired a new phase associated with the use of distributed information and sensory systems and consists in the transition from application of separate sensors and devices to the construction of modular information subsystems, which provide the availability of various data sources and complex methods of information processing. The purpose of the article is to investigate the ways to increase the autonomy of the land-mobile robotic complexes using in a non-deterministic conditions of modern combat. Relevance of researches is connected with the necessity of creation of highly effective information and control systems in the perspective robotic means for the needs of Land Forces of Ukraine. The development of the Armed Forces of Ukraine management system based on the criteria adopted by the EU and NATO member states is one of the main directions of increasing the effectiveness of the use of forces (forces), which involves achieving the principles and standards necessary for Ukraine to become a member of the EU and NATO. The inherent features of achieving these criteria will be the transition to a reduction of tasks of the combined-arms units and the large-scale use of high-precision weapons and land remote-controlled robotic devices. According to the views of the leading specialists in the field of robotics, the automation of information subsystems and components of the land-mobile robotic complexes can increase safety, reliability, error-tolerance and the effectiveness of the use of robotic means by standardizing the necessary actions with minimal human intervention, that is, a significant increase in the autonomy of the land-mobile robotic complexes for the needs of Land Forces of Ukraine.

Stirring and aeration system for the upgrading of small waste water treatment plants

1994 ◽  
Vol 29 (12) ◽  
pp. 149-156 ◽  
Author(s):  
Marcus Höfken ◽  
Katharina Zähringer ◽  
Franz Bischof
Keyword(s):  
Waste Water ◽  
Water Treatment ◽  
Large Scale ◽  
Waste Water Treatment ◽  
Water Treatment Plants ◽  
Waste Water Treatment Plants ◽  
Basic Fluid ◽  
Aeration System ◽  
Technical Realization ◽  
Wide Range

A novel agitating system has been developed which allows for individual or combined operation of stirring and aeration processes. Basic fluid mechanical considerations led to the innovative hyperboloid design of the stirrer body, which ensures high efficiencies in the stirring and the aeration mode, gentle circulation with low shear forces, excellent controllability, and a wide range of applications. This paper presents the basic considerations which led to the operating principle, the technical realization of the system and experimental results in a large-scale plant. The characteristics of the system and the differences to other stirring and aeration systems are illustrated. Details of the technical realization are shown, which conform to the specific demands of applications in the biological treatment of waste water. Special regard is given to applications in the upgrading of small compact waste water treatment plants.

Thin structure of heterogeneous and multiphase fluid flows

2012 ◽  
Vol 9 (1) ◽  
pp. 175-180
Author(s):  
Yu.D. Chashechkin
Keyword(s):  
Large Scale ◽  
Fundamental System ◽  
Fluid Flows ◽  
Regular Solutions ◽  
Flow Models ◽  
Group Methods ◽  
Wide Range ◽  
Thin Structure ◽  
Multiphase Fluid ◽  
Complete Solutions

According to the results of visualization of streams, the existence of structures in a wide range of scales is noted: from galactic to micron. The use of a fundamental system of equations is substantiated based on the results of comparing symmetries of various flow models with the usage of theoretical group methods. Complete solutions of the system are found by the methods of the singular perturbations theory with a condition of compatibility, which determines the characteristic equation. A comparison of complete solutions with experimental data shows that regular solutions characterize large-scale components of the flow, a rich family of singular solutions describes formation of the thin media structure. Examples of calculations and observations of stratified, rotating and multiphase media are given. The requirements for the technique of an adequate experiment are discussed.

Integrative Data Analysis from a Unifying Research Synthesis Perspective

2018 ◽  
Author(s):  
Eun-Young Mun ◽  
Anne E. Ray
Keyword(s):  
Data Analysis ◽  
Large Scale ◽  
Research Synthesis ◽  
Alcohol Intervention ◽  
Data Set ◽  
Integrative Data Analysis ◽  
Level Data ◽  
Model Complex ◽  
Wide Range ◽  
Individual Participant

Integrative data analysis (IDA) is a promising new approach in psychological research and has been well received in the field of alcohol research. This chapter provides a larger unifying research synthesis framework for IDA. Major advantages of IDA of individual participant-level data include better and more flexible ways to examine subgroups, model complex relationships, deal with methodological and clinical heterogeneity, and examine infrequently occurring behaviors. However, between-study heterogeneity in measures, designs, and samples and systematic study-level missing data are significant barriers to IDA and, more broadly, to large-scale research synthesis. Based on the authors’ experience working on the Project INTEGRATE data set, which combined individual participant-level data from 24 independent college brief alcohol intervention studies, it is also recognized that IDA investigations require a wide range of expertise and considerable resources and that some minimum standards for reporting IDA studies may be needed to improve transparency and quality of evidence.

Quantum Optomechanics and Nanomechanics

2020 ◽  
Keyword(s):  
Gravitational Wave ◽  
Summer School ◽  
Large Scale ◽  
Quantum Noise ◽  
Foundations Of Quantum Mechanics ◽  
Wide Range ◽  
Measurement Laser ◽  
Quantum Limits ◽  
Quantum Optomechanics ◽  
Quantum Ground State

The Les Houches Summer School 2015 covered the emerging fields of cavity optomechanics and quantum nanomechanics. Optomechanics is flourishing and its concepts and techniques are now applied to a wide range of topics. Modern quantum optomechanics was born in the late 70s in the framework of gravitational wave interferometry, initially focusing on the quantum limits of displacement measurements. Carlton Caves, Vladimir Braginsky, and others realized that the sensitivity of the anticipated large-scale gravitational-wave interferometers (GWI) was fundamentally limited by the quantum fluctuations of the measurement laser beam. After tremendous experimental progress, the sensitivity of the upcoming next generation of GWI will effectively be limited by quantum noise. In this way, quantum-optomechanical effects will directly affect the operation of what is arguably the world’s most impressive precision experiment. However, optomechanics has also gained a life of its own with a focus on the quantum aspects of moving mirrors. Laser light can be used to cool mechanical resonators well below the temperature of their environment. After proof-of-principle demonstrations of this cooling in 2006, a number of systems were used as the field gradually merged with its condensed matter cousin (nanomechanical systems) to try to reach the mechanical quantum ground state, eventually demonstrated in 2010 by pure cryogenic techniques and a year later by a combination of cryogenic and radiation-pressure cooling. The book covers all aspects—historical, theoretical, experimental—of the field, with its applications to quantum measurement, foundations of quantum mechanics and quantum information. Essential reading for any researcher in the field.

Sign in / Sign up

Export Citation Format

Share Document