scholarly journals Linear relativistic thermoelastic rod

2020 ◽  
Vol 17 (04) ◽  
pp. 863-882
Author(s):  
Anne T. Franzen ◽  
José Natário
Keyword(s):  
Heat Waves ◽  
Hyperbolic Equations ◽  
Classical System ◽  
Propagation Speed ◽  
The Other ◽  
Heat Conducting ◽  
Energy Integral ◽  
Elastic Rod ◽  
Fourier Decomposition ◽  
Finite Propagation Speed

We derive and analyze the linearized hyperbolic equations describing a relativistic heat-conducting elastic rod. We construct a decreasing energy integral for these equations, compute the associated characteristic propagation speeds and prove that the solutions decay in time by using a Fourier decomposition. For comparison purposes, we obtain analogous results for the classical system with heat waves, in which the finite propagation speed of heat is kept but the other relativistic terms are neglected and also for the usual classical system.

Local existence and singularities formation for isothermal relativistic radiation hydrodynamics equations

2016 ◽  
Vol 13 (04) ◽  
pp. 661-683
Author(s):  
Yongcai Geng
Keyword(s):  
Blow Up ◽  
Hyperbolic Equations ◽  
Local Existence ◽  
Three Dimensional ◽  
Propagation Speed ◽  
Smooth Solutions ◽  
Nonlinear Hyperbolic Equations ◽  
The Cauchy Problem ◽  
Finite Propagation Speed ◽  
Hydrodynamics Equations

We study the Cauchy problem for multi-dimensional compressible relativistic hydrodynamics in the presence of a radiation field. First, based on the theory of quasilinear symmetric hyperbolic, we establish the local existence of smooth solutions for both non-vacuum and vacuum cases. Next, in the spirit of Sideris’ work [T. Sideris, Formation of singularities of solutions to nonlinear hyperbolic equations, Arch. Ration. Mech. Anal. 86 (1984) 369–381; T. Sideris, Formation of singularities in three-dimensional compressible fluids, Comm. Math. Phys. 101 (1985) 475–485], we show that smooth solutions blow-up in finite time if the initial data is compactly supported and large enough. Compared with the previous work, the main difficulties of the first problem lie in two aspects, we must first deal with the source terms relying on radiative quantities, and we also need to solve out the new coefficients matrices under the Lorentz transformation for vacuum case. The second difficulty arises on how to verifying that the smooth solution has finite propagation speed..

scholarly journals Time-Delay Identification Using Multiscale Ordinal Quantifiers

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 969
Author(s):  
Miguel C. Soriano ◽  
Luciano Zunino
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Real World ◽  
Propagation Speed ◽  
Real World Data ◽  
External Observer ◽  
The North ◽  
Weather Phenomenon ◽  
The North Atlantic Oscillation ◽  
Finite Propagation Speed

Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon.

Statics Analysis of the Mechanical Model of Nucleosome

2011 ◽  
Vol 343-344 ◽  
pp. 661-667 ◽  
Author(s):  
Yun Xue ◽  
De Wei Weng ◽  
Gang Ming Gong
Keyword(s):  
Mechanical Model ◽  
The Other ◽  
Elastic Rod ◽  
Equilibrium Equations ◽  
Constraint Force ◽  
Precession Angle ◽  
Nutation Angle ◽  
Analytic Expression ◽  
Set Up ◽  
Calculated Analysis

Mechanical model of nucleoside and its equilibrium equations are set up, and the mechanical properties on the equilibrium position are analyzed. In the case constraint force and electrostatic attraction between cylinder OH and elastic rod are balanced, the analytic expression of nutation angle of the section and its conditions of existence are given. It is show that the cylinder OH can maintain equilibrium at any range of the precession angle. In the other case when unbanced, there is phenomenon of separation of elastic rod from cylinder OH in the spiral wound 2 circles, and numerical solution of the precession angle at separation points are calculated. Analysis of equilibrium of cylinder H1 illustrates that the generatrix of cylinder H1 and OH are not parallel, and the angle between them is obtained

Generalized hydrodynamics and heat waves

1992 ◽  
Vol 70 (1) ◽  
pp. 62-71 ◽  
Author(s):  
R. E. Khayat ◽  
Byung Chan Eu
Keyword(s):  
Thermal Conductivity ◽  
Evolution Equations ◽  
Pulse Propagation ◽  
Heat Waves ◽  
Fluid Dynamic ◽  
Propagation Speed ◽  
Heat Pulse ◽  
Irreversible Processes ◽  
Large Temperature ◽  
Generalized Hydrodynamics

By using the evolution equations of generalized hydrodynamics we investigate heat-pulse propagation in a Lennard–Jones liquid contained in the annulus between two concentric cylinders at different temperatures. It is found that the heat pulse propagates as a wave of a finite speed when a composite fluid dynamic number [Formula: see text] that depends on the thermal conductivity and wall temperature ratio is above a critical value, but in the subcritical region the heat pulse propagates diffusively as if predicted by a parabolic differential equation with an infinite speed of propagation. Therefore the question of the hyperbolicity of the system of differential (evolution) equations used is mainly determined by the parameter [Formula: see text]. This implies that the hyperbolicity of evolution equations, i.e., the finiteness of pulse-propagation speed, cannot be the main reason for extending the thermodynamics of irreversible processes as believed by some authors in the literature. This study indicates that for a liquid of high thermal conductivity or a large temperature difference the Fourier law of heat conduction is inadequate for use in the description of the temporal evolution of heat and a suitable generalization of hydrodynamics is necessary. The generalized hydrodynamic equations presented in this and previous papers are examples for such a generalization.

scholarly journals Efficient location strategy for airport surveillance using Mode-S multilateration systems

2012 ◽  
Vol 4 (2) ◽  
pp. 209-216 ◽  
Author(s):  
Ivan A. Mantilla-Gaviria ◽  
Mauro Leonardi ◽  
Gaspare Galati ◽  
Juan V. Balbastre-Tejedor ◽  
Elías de Los Reyes Davó
Keyword(s):  
Lower Bound ◽  
Location Problem ◽  
Hyperbolic Equations ◽  
Classical System ◽  
Regularization Methods ◽  
Location Strategy ◽  
Tikhonov Method ◽  
Cramer Rao Lower Bound ◽  
Bound Analysis

In this paper, the use of regularization methods to solve the location problem in multilateration systems, using Mode-S signals, is studied, evaluated, and developed. The Tikhonov method has been implemented as a first application to solve the classical system of hyperbolic equations in multilateration systems. Some simulations are obtained and the results are compared with those obtained by the well-established Taylor linearization and with the Cramér–Rao lower bound analysis. Significant improvements, for the accuracy, convergence, and the probability of location, are found for the application of the Tikhonov method.

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