scholarly journals Multiple Steady States in Ice-Water-Till Systems

1990 ◽  
Vol 14 ◽  
pp. 1-5 ◽  
Author(s):  
Richard B. Alley
Keyword(s):  
Steady State ◽  
Ice Sheet ◽  
Steady States ◽  
The Other ◽  
Surface Slope ◽  
Dimensional Model ◽  
Climatic Forcing ◽  
Fixed Boundary ◽  
One Dimensional ◽  
Ice Water

An ice sheet with fixed boundary conditions may have two steady configurations, as shown by a new one-dimensional model including the physics and continuity of ice, water, and deforming subglacial till. In one steady state, a steep surface slope causes rapid internal ice shearing but forces basal water through subglacial aquifers, suppressing basal velocity; in the other steady state, a gentle surface slope causes only slow ice shearing but allows water to lubricate the ice-bed interface and cause rapid basal velocities. Small climatic forcing may cause large ice-sheet response during a switch between steady states.

scholarly journals Multiple Steady States in Ice-Water-Till Systems

1990 ◽  
Vol 14 ◽  
pp. 1-5 ◽  
Author(s):  
Richard B. Alley
Keyword(s):  
Steady State ◽  
Ice Sheet ◽  
Steady States ◽  
The Other ◽  
Surface Slope ◽  
Dimensional Model ◽  
Climatic Forcing ◽  
Fixed Boundary ◽  
One Dimensional ◽  
Ice Water

An ice sheet with fixed boundary conditions may have two steady configurations, as shown by a new one-dimensional model including the physics and continuity of ice, water, and deforming subglacial till. In one steady state, a steep surface slope causes rapid internal ice shearing but forces basal water through subglacial aquifers, suppressing basal velocity; in the other steady state, a gentle surface slope causes only slow ice shearing but allows water to lubricate the ice-bed interface and cause rapid basal velocities. Small climatic forcing may cause large ice-sheet response during a switch between steady states.

POVERTY TRAPS AND INFERIOR GOODS IN A DYNAMIC HECKSCHER–OHLIN MODEL

2012 ◽  
Vol 17 (6) ◽  
pp. 1227-1251 ◽  
Author(s):  
Eric W. Bond ◽  
Kazumichi Iwasa ◽  
Kazuo Nishimura
Keyword(s):  
Economic Theory ◽  
Steady State ◽  
World Economy ◽  
Steady States ◽  
The Other ◽  
Poverty Traps ◽  
Poverty Trap ◽  
Multiple Steady States ◽  
The World ◽  
State Capital

We extend the dynamic Heckscher–Ohlin model in Bond et al. [Economic Theory(48, 171–204, 2011)] and show that if the labor-intensive good is inferior, then there may exist multiple steady states in autarky and poverty traps can arise. Poverty traps for the world economy, in the form of Pareto-dominated steady states, are also shown to exist. We show that the opening of trade can have the effect of pulling the initially poorer country out of a poverty trap, with both countries having steady state capital stocks exceeding the autarky level. However, trade can also pull an initially richer country into a poverty trap. These possibilities are a sharp contrast with dynamic Heckscher–Ohlin models with normality in consumption, where the country with the larger (smaller) capital stock than the other will reach a steady state where the level of welfare is higher (lower) than in the autarkic steady state.

Stability Considerations in Thermoelastic Contact

1980 ◽  
Vol 47 (4) ◽  
pp. 871-874 ◽  
Author(s):  
J. R. Barber ◽  
J. Dundurs ◽  
M. Comninou
Keyword(s):  
Steady State ◽  
Perturbation Method ◽  
Energy Function ◽  
First Principles ◽  
Dimensional Model ◽  
Contact Conditions ◽  
One Dimensional ◽  
Thermoelastic Contact ◽  
The Stability ◽  
Steady State Solutions

A simple one-dimensional model is described in which thermoelastic contact conditions give rise to nonuniqueness of solution. The stability of the various steady-state solutions discovered is investigated using a perturbation method. The results can be expressed in terms of the minimization of a certain energy function, but the authors have so far been unable to justify the use of such a function from first principles in view of the nonconservative nature of the system.

scholarly journals Action minimization and macroscopic interface motion under forced displacement

2018 ◽  
Vol 24 (2) ◽  
pp. 765-792 ◽  
Author(s):  
Panagiota Birmpa ◽  
Dimitrios Tsagkarogiannis
Keyword(s):  
Stochastic Process ◽  
Evolution Equation ◽  
Fixed Time ◽  
Companion Paper ◽  
The Other ◽  
Final Position ◽  
Dimensional Model ◽  
Interface Motion ◽  
One Dimensional ◽  
Non Local

We study an one dimensional model where an interface is the stationary solution of a mesoscopic non local evolution equation which has been derived by a microscopic stochastic spin system. Deviations from this evolution equation can be quantified by obtaining the large deviations cost functional from the underlying stochastic process. For such a functional, derived in a companion paper, we investigate the optimal way for a macroscopic interface to move from an initial to a final position distant by R within fixed time T. We find that for small values of R∕T the interface moves with a constant speed, while for larger values there appear nucleations of the other phase ahead of the front.

Experimental studies of the propagation of combustion in solids

1992 ◽  
Vol 339 (1654) ◽  
pp. 387-394 ◽  
Keyword(s):  
Heat Transfer ◽  
Thermal Analysis ◽  
Steady State ◽  
Chemical Kinetics ◽  
Profile Analysis ◽  
Numerical Models ◽  
Experimental Studies ◽  
Dimensional Model ◽  
Thermal Methods ◽  
One Dimensional

The application of thermal methods to the study of steady-state combustion is described. Such methods provide a route to information on heat transfer and chemical kinetics which forms a basis for the implementation of numerical models. The experimental results from thermal analysis and temperature profile analysis have been examined within the context of a simple pseudo one-dimensional model of propagation offering some confirmation of the validity of the approach.

Steady-State Bifurcation for a Biological Depletion Model

2016 ◽  
Vol 26 (04) ◽  
pp. 1650066 ◽  
Author(s):  
Yan’e Wang ◽  
Jianhua Wu ◽  
Yunfeng Jia
Keyword(s):  
Steady State ◽  
Bifurcation Theory ◽  
Steady States ◽  
Two Dimensional ◽  
Implicit Function ◽  
Flux Boundary Condition ◽  
One Dimensional ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Theoretical Results

A two-species biological depletion model in a bounded domain is investigated in which one species is a substrate and the other is an activator. Firstly, under the no-flux boundary condition, the asymptotic stability of constant steady-states is discussed. Secondly, by viewing the feed rate of the substrate as a parameter, the steady-state bifurcations from constant steady-states are analyzed both in one-dimensional kernel case and in two-dimensional kernel case. Finally, numerical simulations are presented to illustrate our theoretical results. The main tools adopted here include the stability theory, the bifurcation theory, the techniques of space decomposition and the implicit function theorem.

Influence of Support Compliance and Residual Stress on the Shape of Doubly-Supported Surface-Micromachined Beams

1999 ◽  
Author(s):  
Mauro J. Kobrinsky ◽  
Erik R. Deutsch ◽  
Stephen D. Senturia
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Finite Element Method ◽  
Residual Stress ◽  
Gradual Increase ◽  
The Other ◽  
Elastic Model ◽  
Dimensional Model ◽  
Stable States ◽  
One Dimensional

Abstract Doubly-supported surface-micromachined beams are increasingly used to study the mechanical properties of thin films. Residual stresses in the beams cause significant vertical deflections, which affect the performance of these devices. We present here both experimental results for doubly-supported polysilicon surface-micromachined beams, and an elastic model of the devices that takes into account the compliance of the supports and the geometrical non-linear dependence of the vertical deflections on the stress in the beam. An elastic one-dimensional model was used for the beams, and the response of the supports to forces and moments was obtained using Finite Element Method simulations. The model explains a previously observed gradual increase of the maximum vertical deflections of the beams with increasing length at a given constant residual stress, and, in agreement with experimental observations, predicts two stable states for compressively stressed beams: one with the beam bent up, the other down.

A Numerical Study of High Temperature and High Velocity Gaseous Hydrogen Flow in a Cooling Channel of a Nuclear Thermal Rocket Core

2014 ◽  
Author(s):  
K. M. Akyuzlu
Keyword(s):  
Steady State ◽  
Gaseous Hydrogen ◽  
Hydrodynamic Characteristics ◽  
Two Dimensional ◽  
Cooling Channel ◽  
Fuel Cladding ◽  
Dimensional Model ◽  
One Dimensional ◽  
Hydrogen Flow ◽  
Cooling Channels

Two mathematical models (a one-dimensional and a two-dimensional) were adopted to study, numerically, the thermal hydrodynamic characteristics of flow inside the cooling channels of a Nuclear Thermal Rocket (NTR) engine. In the present study, only a single one of the cooling channels of the reactor core is simulated. The one-dimensional model adopted here assumes the flow in this cooling channel to be steady, compressible, turbulent, and subsonic. The physics based mathematical model of the flow in the channel consists of conservation of mass, momentum, and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The working fluid (gaseous hydrogen) is assumed to be compressible through a simple ideal gas relation. The physical and transport properties of the hydrogen is assumed be temperature dependent. The governing equations of the compressible flow in cooling channels are discretized using the second order accurate MacCormack finite difference scheme. Convergence and grid independence studies were done to determine the optimum computational cell mesh size and computational time increment needed for the present simulations. The steady state results of the proposed model were compared to the predictions by a commercial CFD package (Fluent.) The two-dimensional CFD solution was obtained in two domains: the coolant (gaseous hydrogen) and the ZrC fuel cladding. The wall heat flux which varied along the channel length (as described by the nuclear variation in the nuclear power generation) was given as an input. Numerical experiments were carried out to simulate the thermal and hydrodynamic characteristics of the flow inside a single cooling channel of the reactor for a typical NERVA type NTR engine where the inlet mass flow rate was given as an input. The time dependent heat generation and its distribution due to the nuclear reaction taking place in the fuel matrix surrounding the cooling channel. Numerical simulations of flow and heat transfer through the cooling channels were generated for steady state gaseous hydrogen flow. The temperature, pressure, density, and velocity distributions of the hydrogen gas inside the coolant channel are then predicted by both one-dimensional and two-dimensional model codes. The steady state predictions of both models were compared to the existing results and it is concluded that both models successfully predict the steady state fluid temperature and pressure distributions experienced in the NTR cooling channels. The two dimensional model also predicts, successfully, the temperature distribution inside the nuclear fuel cladding.

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