Recurrence relations and time evolution in the three-dimensional Sawada model

1984 ◽  
Vol 30 (11) ◽  
pp. 6756-6758 ◽  
Author(s):  
M. Howard Lee ◽  
J. Hong
Keyword(s):  
Time Evolution ◽  
Recurrence Relations ◽  
Three Dimensional

scholarly journals Study of a temperature gradient metamorphism of snow from 3-D images: time evolution of microstructures, physical properties and their associated anisotropy

2014 ◽  
Vol 8 (6) ◽  
pp. 2255-2274 ◽  
Author(s):  
N. Calonne ◽  
F. Flin ◽  
C. Geindreau ◽  
B. Lesaffre ◽  
S. Rolland du Roscoat
Keyword(s):  
Temperature Gradient ◽  
Physical Properties ◽  
Time Evolution ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Large Set ◽  
Correlation Lengths ◽  
Snow Properties ◽  
Cold Room ◽  
Anisotropy Coefficients

Abstract. We carried out a study to monitor the time evolution of microstructural and physical properties of snow during temperature gradient metamorphism: a snow slab was subjected to a constant temperature gradient in the vertical direction for 3 weeks in a cold room, and regularly sampled in order to obtain a series of three-dimensional (3-D) images using X-ray microtomography. A large set of properties was then computed from this series of 3-D images: density, specific surface area, correlation lengths, mean and Gaussian curvature distributions, air and ice tortuosities, effective thermal conductivity, and intrinsic permeability. Whenever possible, specific attention was paid to assess these properties along the vertical and horizontal directions, and an anisotropy coefficient defined as the ratio of the vertical over the horizontal values was deduced. The time evolution of these properties, as well as their anisotropy coefficients, was investigated, showing the development of a strong anisotropic behavior during the experiment. Most of the computed physical properties of snow were then compared with two analytical estimates (self-consistent estimates and dilute beds of spheroids) based on the snow density, and the size and anisotropy of the microstructure through the correlation lengths. These models, which require only basic microstructural information, offer rather good estimates of the properties and anisotropy coefficients for our experiment without any fitting parameters. Our results highlight the interplay between the microstructure and physical properties, showing that the physical properties of snow subjected to a temperature gradient cannot be described accurately using only isotropic parameters such as the density and require more refined information. Furthermore, this study constitutes a detailed database on the evolution of snow properties under a temperature gradient, which can be used as a guideline and a validation tool for snow metamorphism models at the micro- or macroscale.

scholarly journals Time evolution of companies towards a stable scaling curve obtained from flow diagrams in three-dimensional phase space

2019 ◽  
Vol 21 (4) ◽  
pp. 043038
Author(s):  
Yuh Kobayashi ◽  
Hideki Takayasu ◽  
Shlomo Havlin ◽  
Misako Takayasu
Keyword(s):  
Phase Space ◽  
Time Evolution ◽  
Three Dimensional ◽  
Dimensional Phase Space ◽  
Flow Diagrams

Stabilization of Filament Production Rate for Screw Extrusion-Based Polymer Three-Dimensional-Printing

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Shumon Koga ◽  
David Straub ◽  
Mamadou Diagne ◽  
Miroslav Krstic
Keyword(s):  
Differential Equation ◽  
3D Printing ◽  
Temperature Profile ◽  
Time Evolution ◽  
Output Feedback ◽  
Three Dimensional ◽  
Output Feedback Control ◽  
Raw Material ◽  
Interface Position ◽  
Screw Extrusion

Abstract Polymer three-dimensional (3D)-printing has been commercialized rapidly during recent years; however, there remains a matter of improving the manufacturing speed. Screw extrusion has a strong potential to fasten the process through the simultaneous operation of the filament production and the deposition. This paper develops a control algorithm for screw extrusion-based 3D printing of thermoplastic materials through an observer-based output feedback design. We consider the thermodynamic model describing the time evolution of the temperature profile of an extruded polymer by means of a partial differential equation (PDE) defined on the time-varying domain. The time evolution of the spatial domain is governed by an ordinary differential equation that reflects the dynamics of the position of the phase change interface between polymer granules and molten polymer deposited as a molten filament. The steady-state profile of the distributed temperature along the extruder is obtained when the desired setpoint for the interface position is prescribed. To enhance the feasibility of our previous design, we develop a PDE observer to estimate the temperature profile via measured values of surface temperature and the interface position. An output feedback control law considering a cooling mechanism at the boundary inlet as an actuator is proposed. In extruders, the control of raw material temperature is commonly achieved using preconditioners as part of the inlet feeding mechanism. For some given screw speeds that correspond to slow and fast operating modes, numerical simulations are conducted to prove the performance of the proposed controller. The convergence of the interface position to the desired setpoint is achieved under physically reasonable temperature profiles.

scholarly journals Multi-scale dynamics of magnetic flux tubes and inverse magnetic energy transfer

2020 ◽  
Vol 86 (4) ◽  
Author(s):  
Muni Zhou ◽  
Nuno F. Loureiro ◽  
Dmitri A. Uzdensky
Keyword(s):  
Magnetic Flux ◽  
Time Evolution ◽  
Magnetic Energy ◽  
Numerical Study ◽  
Three Dimensional ◽  
Early Time ◽  
Small Scale ◽  
Flux Tubes ◽  
Seed Field ◽  
Magnetic Flux Tubes

We report on an analytical and numerical study of the dynamics of a three-dimensional array of identical magnetic flux tubes in the reduced-magnetohydrodynamic description of the plasma. We propose that the long-time evolution of this system is dictated by flux-tube mergers, and that such mergers are dynamically constrained by the conservation of the pertinent (ideal) invariants, viz. the magnetic potential and axial fluxes of each tube. We also propose that in the direction perpendicular to the merging plane, flux tubes evolve in a critically balanced fashion. These notions allow us to construct an analytical model for how quantities such as the magnetic energy and the energy-containing scale evolve as functions of time. Of particular importance is the conclusion that, like its two-dimensional counterpart, this system exhibits an inverse transfer of magnetic energy that terminates only at the system scale. We perform direct numerical simulations that confirm these predictions and reveal other interesting aspects of the evolution of the system. We find, for example, that the early time evolution is characterized by a sharp decay of the initial magnetic energy, which we attribute to the ubiquitous formation of current sheets. We also show that a quantitatively similar inverse transfer of magnetic energy is observed when the initial condition is a random, small-scale magnetic seed field.

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