scholarly journals A mixture theory for geophysical fluids

2004 ◽  
Vol 11 (1) ◽  
pp. 75-82 ◽  
Author(s):  
A. C. Eringen
Keyword(s):  
Constitutive Equations ◽  
Degrees Of Freedom ◽  
Oil Spills ◽  
Initial Conditions ◽  
Mixture Theory ◽  
Continuum Theory ◽  
Second Law Of Thermodynamics ◽  
Heat Conducting ◽  
Field Equations ◽  
The Individual

Abstract. A continuum theory is developed for a geophysical fluid consisting of two species. Balance laws are given for the individual components of the mixture, modeled as micropolar viscous fluids. The continua allow independent rotational degrees of freedom, so that the fluids can exhibit couple stresses and a non-symmetric stress tensor. The second law of thermodynamics is used to develop constitutive equations. Linear constitutive equations are constituted for a heat conducting mixture, each species possessing separate viscosities. Field equations are obtained and boundary and initial conditions are stated. This theory is relevant to an atmospheric mixture consisting of any two species from rain, snow and/or sand. Also, this is a continuum theory for oceanic mixtures, such as water and silt, or water and oil spills, etc.

scholarly journals NONEXISTENCE OF IRREVERSIBLE PROCESSES IN COMPACT SPACE–TIME

2007 ◽  
Vol 22 (32) ◽  
pp. 6227-6241 ◽  
Author(s):  
HOLGER B. NIELSEN ◽  
MASAO NINOMIYA
Keyword(s):  
Compact Space ◽  
Initial Conditions ◽  
Physical Space ◽  
Second Law Of Thermodynamics ◽  
Space Time ◽  
Classical Field ◽  
Irreversible Processes ◽  
Second Law ◽  
Field Equations ◽  
Time Direction

It is shown that if physical space–time were truly compact there would only be of the order-of-one solutions to the classical field equations with a weighting to be explained. But that would not allow any peculiar choice of initial conditions that could support a nontrivial second law of thermodynamics. We present a no-go theorem: irreversible processes would be extremely unlikely to occur for the almost unique solution for the intrinsically compact space–time world, although irreversible processes are well known to occur in general. What we assume here — the compact space–time — is that universe could not exist eternally. In other word if universe stays on forever (i.e. noncompact in time direction) our no-go theorem is not applicable.

scholarly journals Nonlinear Behavior of a Magnetic Bearing System

1995 ◽  
Vol 117 (3) ◽  
pp. 582-588 ◽  
Author(s):  
L. N. Virgin ◽  
T. F. Walsh ◽  
J. D. Knight
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
Analytical Techniques ◽  
Magnetic Bearing ◽  
Forced Response ◽  
The Mathematical Model ◽  
Two Degree Of Freedom ◽  
Sensitivity To Initial Conditions ◽  
Bearing System

This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bearings and subject to rotating unbalance and feedback control. Geometric coupling between the degrees of freedom leads to a pair of nonlinear ordinary differential equations, which are then solved using both numerical simulation and approximate analytical techniques. The system exhibits a variety of interesting and somewhat unexpected phenomena including various amplitude driven bifurcational events, sensitivity to initial conditions, and the complete loss of stability associated with the escape from the potential well in which the system can be thought to be oscillating. An approximate criterion to avoid this last possibility is developed based on concepts of limiting the response of the system. The present paper may be considered as an extension to an earlier study by the same authors, which described the practical context of the work, free vibration, control aspects, and derivation of the mathematical model.

Full Implicit Integrate Solution to the Coupled Neutronics/Thermal-Hydraulics Problems

2013 ◽  
Author(s):  
Han Zhang ◽  
Fu Li
Keyword(s):  
Nuclear Reactor ◽  
Reactor Core ◽  
Thermal Hydraulics ◽  
Field Equations ◽  
Krylov Method ◽  
Tightly Coupled ◽  
Physical Insight ◽  
Second Order Convergence ◽  
The Individual ◽  
Integrate Solution

The traditional solution of the coupled neutronics/ thermal-hydraulics problems has typically been performed by solving the individual field separately and then transferring information between each other. In this paper, full implicit integrate solution to the coupled neutronics/ thermal-hydraulic problem is investigated. There are two advantages compared with the traditional method, which are high temporal accuracy and stability. The five equations of single-phase flow, the solid heat conduction and the neutronics are employed as a simplified model of a nuclear reactor core. All these field equations are solved together in a tightly coupled, nonlinear fashion. Firstly, Newton-based method is employed to solve nonlinear systems due to its local second-order convergence rate. And then the Krylov iterative method is used to solve the linear systems which are from the Newton linearization. The two procedures above are the so-called Newton-Krylov method. Furthermore, in order to improve the performance of the Krylov method, physics-based preconditioner is employed, which is constructed by the physical insight. Finally, several Newton-Krylov solution approaches are carried out to compare the performance of the coupled neutronics / thermal-hydraulic equations.

A Quasi-three-dimensional Finite-volume Shallow Water Model for Green Water on Deck

2013 ◽  
Vol 57 (03) ◽  
pp. 125-140
Author(s):  
Daniel A. Liut ◽  
Kenneth M. Weems ◽  
Tin-Guen Yen
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Green Water ◽  
Water Model ◽  
Ship Motions ◽  
Shallow Water Model

A quasi-three-dimensional hydrodynamic model is presented to simulate shallow water phenomena. The method is based on a finite-volume approach designed to solve shallow water equations in the time domain. The nonlinearities of the governing equations are considered. The methodology can be used to compute green water effects on a variety of platforms with six-degrees-of-freedom motions. Different boundary and initial conditions can be applied for multiple types of moving platforms, like a ship's deck, tanks, etc. Comparisons with experimental data are discussed. The shallow water model has been integrated with the Large Amplitude Motions Program to compute the effects of green water flow over decks within a time-domain simulation of ship motions in waves. Results associated to this implementation are presented.

A Local Approach for Computing Smooth B-spline Surfaces for Arbitrary Quadrilateral Base Meshes

2021 ◽  
pp. 1-28
Author(s):  
Dennis Mosbach ◽  
Katja Schladitz ◽  
Bernd Hamann ◽  
Hans Hagen
Keyword(s):  
Degrees Of Freedom ◽  
Tangent Plane ◽  
Local Approach ◽  
Approximation Process ◽  
Surface Approximation ◽  
B Spline ◽  
Spline Surfaces ◽  
Continuous Surface ◽  
Normal Vectors ◽  
The Individual

Abstract We present a method for approximating surface data of arbitrary topology by a model of smoothly connected B-spline surfaces. Most of the existing solutions for this problem use constructions with limited degrees of freedom or they address smoothness between surfaces in a post-processing step, often leading to undesirable surface behavior in proximity of the boundaries. Our contribution is the design of a local method for the approximation process. We compute a smooth B-spline surface approximation without imposing restrictions on the topology of a quadrilateral base mesh defining the individual B-spline surfaces, the used B-spline knot vectors, or the number of B-spline control points. Exact tangent plane continuity can generally not be achieved for a set of B-spline surfaces for an arbitrary underlying quadrilateral base mesh. Our method generates a set of B-spline surfaces that lead to a nearly tangent plane continuous surface approximation and is watertight, i.e., continuous. The presented examples demonstrate that we can generate B-spline approximations with differences of normal vectors along shared boundary curves of less than one degree. Our approach can also be adapted to locally utilize other approximation methods leading to higher orders of continuity.

Sources of morphological variation and organization within and among populations of Balsamorhiza sagittata

1988 ◽  
Vol 66 (1) ◽  
pp. 11-17 ◽  
Author(s):  
K. A. Robson ◽  
R. K. Scagel ◽  
J. Maze
Keyword(s):  
Open Systems ◽  
Second Law Of Thermodynamics ◽  
Population Diversity ◽  
Individual Plant ◽  
Theory Of Evolution ◽  
Plant Parts ◽  
The Individual ◽  
The Relationship ◽  
Balsamorhiza Sagittata ◽  
Two Populations

Comparisons of differences between morphological means of individual plant parts indicate that the greatest source of variation in two populations of Balsamorhiza sagittata is the individual plants within populations; within-population diversity is greater than among-population diversity. Variable covariance and correlations differ between individual plants and there are subgroups of interrelated variables that can be tied to developmental phenomena. The relationship between developmental phenomena and these groups of variables suggests a relationship between organizational, as reflected in variable interrelationships, and ontogenetic variation. These results are not adequately explained by neoDarwinian theory but are explained more comprehensively by a theory of evolution that views biological change over time as an intrinsically driven self-organization, accompanied by an increase in complexity (a manifestation of the "Second Law of Thermodynamics" as it applies to open systems).

Modular Origami Robot Inspired by a Scorpion Tail

2018 ◽  
Author(s):  
Jovana Jovanova ◽  
Maja Anachkova ◽  
Viktor Gavriloski ◽  
Dimitar Petrevski ◽  
Franka Grazhdani ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Basic Structure ◽  
Body Parts ◽  
Main Concept ◽  
Multiple Degrees Of Freedom ◽  
Transparent Layer ◽  
Plastic Foil ◽  
Greater Curvature ◽  
The Individual ◽  
Outer Coating

Arthropod animals like scorpions with modular body parts can be an inspiration for a robot’s structure. The design presented here relays on inter-connected origami towers, but could also be easily disassembled. Each origami tower is fully autonomous and at the same time is part of the robot as a whole. The towers are positioned between two platforms that enable modularity. The scorpion’s tale shape is achieved by the varying platform diameter resulting in cone-like form. Each tower is actuated independently to enable multiple degrees of freedom. Maneuvering with separated units, assists in easier reparation as well as replacement. Detaching the towers into separate parts makes this structure develop more precise movements, since every unit will move autonomously. Therefore, having a higher number of separated movements combined leads to a smooth bionic movement. So, the overall hierarchy will be modular contributing to a greater curvature bending of the whole structure. Actuating and maneuvering the robot in the main concept is done by separated electro motors, built in the platform. The basic structure will be built from thick paper with plastic coatings. The thick paper itself is lightweight, but at the same time flexible. To protect the paper towers, double plastic foil is placed as an outer coating which acts as an origami cover. This transparent layer is elastic hence it can follow and support the individual units’ movements. This work is focused on understanding origami towers kinematics and different combinations of inter-connected towers to achieve multiple degrees of freedom. A conceptual model is developed, supported by CAD and mathematical models. At the end a prototype is presented.

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