scholarly journals Simulation of the dynamics of the Hansbreen tidal glacier (Svalbard) based on the stochastic model

2019 ◽  
Vol 59 (4) ◽  
pp. 452-459
Author(s):  
A. V. Kislov ◽  
A. F. Glazovsky
Keyword(s):  
Langevin Equation ◽  
Temporal Dynamics ◽  
Planck Equation ◽  
Length Change ◽  
Heat Fluxes ◽  
Point Of View ◽  
Stable Equilibrium Position ◽  
Glacier Length ◽  
Interannual Fluctuations ◽  
Normal Law

The dynamics of the Hansbreen tidal glacier (Svalbard) is manifested at different time scales. In addition to the long-term trend, there are noticeable inter-annual fluctuations. And the last ones are precisely the subject of this work. Based on general conclusions of the theory of temporal dynamics of the massive inertial objects, the observed inter-annual changes in the length of the glacier can be explained as a result of the accumulation of anomalies of the heat fluxes and water flows. In spite the fact that the initial model of glacier dynamics is deterministically based on the physical law of conservation of ice mass (the so-called the «minimal model» was used), the model of length change is interpreted as stochastic. From this standpoint, it is the Langevin equation, which includes the effect of random temperature anomalies that can be interpreted as a white noise. From a mathematical point of view, this process is analogous to Brownian motion, i.e. the length of the Hansbreen glacier randomly fluctuates in the vicinity of its stable equilibrium position. Based on the Langevin equation, we passed to the Fokker–Planck equation, the solution of which allowed us to obtain the distribution function of the probabilities of interannual fluctuations of glacier length, which is close to the normal law. It was shown that the possible range of the variability covers the observed interval of the length fluctuations. The pdf is close to normal distribution.

scholarly journals Imperfect Crystals and Dynamical X-ray Diffraction in the Complex Reflectance Plane

1991 ◽  
Vol 44 (6) ◽  
pp. 693 ◽  
Author(s):  
TJ Davis
Keyword(s):  
Stochastic Model ◽  
Parameter Space ◽  
Langevin Equation ◽  
Planck Equation ◽  
Theoretical Framework ◽  
Crystal Defects ◽  
X Rays ◽  
X Ray Diffraction ◽  
Dynamical Diffraction ◽  
X Ray

A theoretical framework is developed to describe the dynamical diffraction of X-rays in perfect and imperfect crystals. The propagation of the X-ray beam inside the crystal is described by the evolution of a set of trajectories in the complex reflectance plane. The trajectory path is determined from a form of the Takagi-Taupin equations and leads naturally to simple forms for the crystal reflectivity for perfect crystals. A stochastic model for the effects of crystal defects is developed in terms of the Langevin equation which leads to a description of diffraction from imperfect crystals as the evolution of densities in a parameter space, described by a Fokker-Planck equation.

scholarly journals Departamento de Ecología Funcional y Aplicada, Instituto de Ecología, Universidad Nacional Autónoma de México

2017 ◽  
pp. 83
Author(s):  
Victor L. Barradas
Keyword(s):  
Energy Balance ◽  
Control Systems ◽  
Environmental Changes ◽  
Heat Fluxes ◽  
Point Of View ◽  
Net Energy ◽  
Sensible Heat ◽  
Species Establishment ◽  
Physical Barriers ◽  
A Site

<p>The deforestation of a site for agriculture and/ or cattle raising purposes changes either microclimate and soil properties. These environmental changes can act as physical barriers which drastically limits tree species establishment in reforestation . From microclimatic point of view, the study of the energy balance plays a key role when the original environment is severely changed. The net energy in a site is mainly dissipated by latent and sensible heat fluxes which are associated to evapotranspiration and thermal regimes,<br />respectively. The analyses of these fluxes allow to design control systems to reduce the high evaporation rates and high temperatures registered in a deforested site. Energy balance, latent and sensible heat fluxes and other components are analysed, and some techniques to manipulate energy balance are also presented.</p>

PROBABILITY DENSITY EVOLUTION EQUATIONS — A HISTORICAL INVESTIGATION

2009 ◽  
Vol 03 (03) ◽  
pp. 209-226 ◽  
Author(s):  
LI JIE ◽  
CHEN JIANBING
Keyword(s):  
Evolution Equation ◽  
Probability Density ◽  
Evolution Equations ◽  
Planck Equation ◽  
Point Of View ◽  
Lagrangian Description ◽  
Density Evolution ◽  
Physical Point ◽  
Probability Density Evolution ◽  
Generalized Probability

The paper aims at clarifying the essential relationship between traditional probability density evolution equations and the generalized probability density evolution equation which is developed by the authors in recent years. Using the principle of preservation of probability as a uniform fundamental, the probability density evolution equations, including the Liouville equation, Fokker–Planck equation and the Dostupov–Pugachev equation, are derived from the physical point of view. It is pointed out that combining with Eulerian or Lagrangian description of the associated dynamical system will lead to different probability density evolution equations. Particularly, when both the principle and dynamical systems are viewed from Lagrangian description, we are led to the generalized probability density evolution equation.

scholarly journals Infinite dimensional Langevin equation and Fokker-Planck equation

1981 ◽  
Vol 81 ◽  
pp. 177-223 ◽  
Author(s):  
Yoshio Miyahara
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Partial Differential Equations ◽  
Langevin Equation ◽  
Planck Equation ◽  
Theory Theory ◽  
Quantum Field ◽  
Filtering Theory ◽  
Infinite Dimensional

Stochastic processes on a Hilbert space have been discussed in connection with quantum field theory, theory of partial differential equations involving random terms, filtering theory in electrical engineering and so forth, and the theory of those processes has greatly developed recently by many authors (A. B. Balakrishnan [1, 2], Yu. L. Daletskii [7], D. A. Dawson [8, 9], Z. Haba [12], R. Marcus [18], M. Yor [26]).

scholarly journals Dynamic Lognormal Shadowing Framework for the Performance Evaluation of Next Generation Cellular Systems

2019 ◽  
Vol 11 (5) ◽  
pp. 106
Author(s):  
Georgios A. Karagiannis ◽  
Athanasios D. Panagopoulos
Keyword(s):  
Performance Evaluation ◽  
Large Scale ◽  
Channel Model ◽  
Temporal Dynamics ◽  
Future Internet ◽  
Point Of View ◽  
Cellular Systems ◽  
Internet Applications ◽  
Spatial Correlation Structure ◽  
Lognormal Shadowing

Performance evaluation tools for wireless cellular systems are very important for the establishment and testing of future internet applications. As the complexity of wireless networks keeps growing, wireless connectivity becomes the most critical requirement in a variety of applications (considered also complex and unfavorable from propagation point of view environments and paradigms). Nowadays, with the upcoming 5G cellular networks the development of realistic and more accurate channel model frameworks has become more important since new frequency bands are used and new architectures are employed. Large scale fading known also as shadowing, refers to the variations of the received signal mainly caused by obstructions that significantly affect the available signal power at a receiver’s position. Although the variability of shadowing is considered mostly spatial for a given propagation environment, moving obstructions may significantly impact the received signal’s strength, especially in dense environments, inducing thus a temporal variability even for the fixed users. In this paper, we present the case of lognormal shadowing, a novel engineering model based on stochastic differential equations that models not only the spatial correlation structure of shadowing but also its temporal dynamics. Based on the proposed spatio-temporal shadowing field we present a computationally efficient model for the dynamics of shadowing experienced by stationary or mobile users. We also present new analytical results for the average outage duration and hand-offs based on multi-dimensional level crossings. Numerical results are also presented for the validation of the model and some important conclusions are drawn.

Performance of the Bond Graph Approach for the Detection and Localization of Faults of a Refrigerator Compartment Containing an Ice Quantity

2018 ◽  
Vol 26 (03) ◽  
pp. 1850028 ◽  
Author(s):  
Abderrahmene Sellami ◽  
Emna Aridhi ◽  
Dhia Mzoughi ◽  
Abdelkader Mami
Keyword(s):  
Bond Graph ◽  
Heat Fluxes ◽  
Point Of View ◽  
Internal Cooling ◽  
Linear Fractional Transformations ◽  
Insulation Failure ◽  
Water Container ◽  
Simulation Results ◽  
Heat Transfers ◽  
Detection And Localization

In this paper, a robust fault diagnosis for a refrigerator compartment containing a quantity of ice using the bond graph (BG) approach is performed by linear fractional transformations (LFTs). The BG model describes heat transfers supported by the amount of ice placed in the refrigerator compartment, as well as a water container. The LFT modeling of BG elements offers advantages from the point of view of structural analysis and data processing implementation. We have introduced four faults, which consist of ice temperature rise, water leakage, insulation failure at the hot walls of the refrigerator and an increase of the internal temperature due to poor door sealing. The faults are in the form of additional heat fluxes. The simulation results show the effectiveness of the proposed method for detecting and localizing faults. In addition, the lack of door sealing has the most influence on the temperatures in the internal cooling space, water, and ice compared to the other faults.

Thermostructural Analyses Supporting the Design of the HYPROB Heat Sink Subscale Breadboard

2014 ◽  
Author(s):  
M. Ferraiuolo ◽  
A. Martucci ◽  
F. Battista ◽  
D. Ricci
Keyword(s):  
Heat Sink ◽  
Structural Integrity ◽  
Specific Impulse ◽  
Thermal Analyses ◽  
High Energy ◽  
Life Cycles ◽  
Heat Fluxes ◽  
Point Of View ◽  
Rocket Engines ◽  
Combustion Enthalpy

Today’s rocket engines regeneratively cooled using high energy cryogenic propellants (e.g. LOX and LH2, LOX and LCH4) play a major role due to the high combustion enthalpy (10–13.4 kJ/kg) and the high specific impulse of these propellants. In the frame of the HYPROB/Bread project, whose main goal is to design build and test a 30 kN regeneratively cooled thrust chamber, a breadboard has been conceived in order to: • investigate the behavior of the injector that will be employed in the full scale final demonstrator, • to obtain a first estimate of the heat flux on the combustion chamber for models validation, • to implement a “battleship” chamber for a first verification of the stability of the combustion The breadboard is called HS (Heat Sink) and it is made of CuCrZr (Copper Chromium Zirconium alloy), Inconel 718 and TZM (Titanium Zirconium Molybdenum alloy). The aim of the present paper is to illustrate the thermostructural design conducted on the breadboard by means of a Finite Element Method code taking into account the viscoplastic behavior of the adopted materials. An optimization process has been carried out in order to keep the structural integrity of the breadboard maximizing the life cycles of the component. Heat fluxes generated by combustion gases have been evaluated by means of CFD quick analyses, while convection and radiation with the external environment have not been considered in order to be as conservative as possible from a thermostructural point of view. Transient thermal analyses and static structural analyses have been performed by means of ANSYS code adopting an axisymmetric model of the chamber. These analyses have demonstrated that the Breadboard can withstand the design goal of 3 thermo-mechanical cycles with a safety factor equal to 4 considering a firing time equal to 3 seconds.

Elementary derivation of the kinetic equation for the two-dimensional guiding centre plasma

1978 ◽  
Vol 19 (1) ◽  
pp. 121-133 ◽  
Author(s):  
Michael Mond ◽  
Georg Knorr
Keyword(s):  
Kinetic Equation ◽  
Langevin Equation ◽  
Time Scale ◽  
Equations Of Motion ◽  
Planck Equation ◽  
Stochastic Equations ◽  
Iteration Scheme ◽  
Two Dimensional ◽  
Hopf Equation ◽  
Rigorous Solution

A kinetic equation for a two-dimensional inviscid hydrodynamic fluid is derived in two ways. First, the equations of motion for the modes of the fluid are interpreted as stochastic equations resembling the Langevin equation. To lowest order a Fokker–Planck equation can be derived which is the kinetic equation for one mode. Secondly, a suitable iteration scheme is applied to the Hopf equation which results in the same kinetic equation. A parameter describing the time scale is arbitrary and cannot be determined by the applied methods alone. It is shown that the kinetic equation satisfies the conservation requirements and relaxes to an equilibrium which is a rigorous solution of the Hopf equation.

scholarly journals Robust identification of harmonic oscillator parameters using the adjoint Fokker–Planck equation

2017 ◽  
Vol 473 (2200) ◽  
pp. 20160894 ◽  
Author(s):  
E. Boujo ◽  
N. Noiray
Keyword(s):  
Temporal Dynamics ◽  
Oscillation Amplitude ◽  
Planck Equation ◽  
Van Der Pol Oscillator ◽  
Thermoacoustic Instabilities ◽  
Fokker Planck Equation ◽  
Forced Oscillators ◽  
Wide Range ◽  
Output Only ◽  
Fokker Planck

We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator’s damping and stiffness properties are postulated, guided by physical understanding of the oscillatory phenomena. The temporal dynamics and the probability density function of the oscillation amplitude are described by a Langevin equation and its associated Fokker–Planck equation, respectively. One method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values, obtained from data processing by taking the short-time limit of the first two transition moments. However, this limit estimation loses robustness in some situations—for instance when the data are band-pass filtered to isolate the spectral contents of the oscillatory phenomena of interest. In this paper, we use a robust alternative where the adjoint Fokker–Planck equation is solved to compute Kramers–Moyal coefficients exactly, and an iterative optimization yields the parameters that best fit the observed statistics simultaneously in a wide range of amplitudes and time scales. The method is illustrated with a stochastic Van der Pol oscillator serving as a prototypical model of thermoacoustic instabilities in practical combustors, where system identification is highly relevant to control.

scholarly journals Photo-electrons and negative ions

1931 ◽  
Vol 134 (824) ◽  
pp. 427-444 ◽  
Keyword(s):  
Carbon Dioxide ◽  
Experimental Investigation ◽  
Applied Field ◽  
Negative Ions ◽  
Point Of View ◽  
Electrons And Ions ◽  
Abnormal Increase ◽  
Normal Law

The normal law connecting the mobility ( k ) of a gas ion with the pressure ( p ) of the gas, is that the product pk is constant. More than 20 years ago Kovarik found that this product showed an abnormal increase in the case of the negative ions formed in air and carbon dioxide when the pressure was lowered below 20 cm. approximately; this result was interpreted as denoting a progressive diminution in the size and mass of the ion as the pressure is reduced. Some years later the author conducted an experimental investigation, from the results of which he concluded that at the lower pressures the carriers of negative electricity consist of two kinds, electrons and ions; the electrons come more and more into evidence as the pressure of the gas is reduced and travel freely under the influence of an applied field without becoming attached to molecules. From this point of view anomalous mobilities will be obtained at lower pressures unless the electrons are separated experimentally from the negative ions. The author found that, when this separation was effected, the mobility law, pk = const., remained valid down to the lowest pressure employed, viz., 0·15 mm.

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