Fixed point convergence and acceleration for steady state population balance modelling of precipitation processes: application to neodymium oxalate

AbstractBy the first welfare theorem, competitive market equilibria belong to the core and hence are Pareto optimal. Letting money be a commodity, this paper turns these two inclusions around. More precisely, by generalizing the second welfare theorem we show that the said solutions may coincide as a common fixed point for one and the same system.Mathematical arguments invoke conjugation, convolution, and generalized gradients. Convexity is merely needed via subdifferentiablity of aggregate “cost”, and at one point only.Economic arguments hinge on idealized market mechanisms. Construed as algorithms, each stops, and a steady state prevails if and only if price-taking markets clear and value added is nil.

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A steady-state analysis of adaptive notch filters realized tith fixed-point arithmetic

1993 IEEE International Symposium on Circuits and Systems ◽

10.1109/iscas.1993.692779 ◽

2005 ◽

Author(s):

S. Nishimura

Keyword(s):

Fixed Point ◽

Steady State ◽

Notch Filters ◽

Steady State Analysis ◽

Fixed Point Arithmetic ◽

Adaptive Notch Filters ◽

Point Arithmetic ◽

State Analysis

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Collrad: A code for calculating the quasi-steady state population densities of excited states of hydrogen-like ions

Computer Physics Communications ◽

10.1016/s0010-4655(84)82609-0 ◽

1984 ◽

Vol 35 ◽

pp. C-398

Author(s):

G.J. Tallents

Keyword(s):

Steady State ◽

Excited States ◽

Quasi Steady State ◽

Population Densities ◽

State Population

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Analytical Investigation of Hopf Bifurcations Occurring in a 1DOF Sliding-Friction Oscillator With Application to Disc-Brake Vibrations

Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2005-84312 ◽

2005 ◽

Cited By ~ 1

Author(s):

Hartmut Hetzler ◽

Wolfgang Seemann ◽

Daniel Schwarzer

Keyword(s):

Fixed Point ◽

Steady State ◽

Limit Cycle ◽

Relative Velocity ◽

Sliding Friction ◽

Analytical Investigation ◽

Stable Region ◽

Stable Steady State ◽

Disc Brake ◽

Stick Slip

This article deals with analytical investigations on stability and bifurcations due to declining dry friction characteristics in the sliding domain of a simple disc-brake model, which is commonly referred to as “mass-on-a-belt”-oscillator. Sliding friction is described in the sense of Coulomb as proportional to the normal force, but with a friction coefficient μS which depends on the relative velocity. For many common friction models this latter dependence on the relative velocity can be described by exponential functions. For such a characteristic the stability and bifurcation behavior is discussed. It is shown, that the system can undergo a subcritical Hopf-bifurcation from an unstable steady-state fixed point to an unstable limit cycle, which separates the basins of the stable steady-state fixed point and the self sustained stick-slip limit cycle. Therefore, only a local examination of the eigenvalues at the steady-state, as is the classical ansatz when investigating conditions for the onset of friction-induced vibrations, may not give the whole picture, since the stable region around the steady state fixed point may be rather small. The analytical results are verified by numerical simulations. Parameter values are chosen for a model which corresponds to a conventional disc-brake.

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