A tuneable array of unique steady-state microfluidic gradients

2013 ◽  
Vol 15 (31) ◽  
pp. 12805 ◽  
Author(s):  
Matthew D. Estes ◽  
Cedric Hurth ◽  
Matthew Barrett ◽  
Frederic Zenhausern
Keyword(s):  
Steady State ◽  
Unique Steady State

scholarly journals THE RICH AND THE POOR IN A SIMPLE MODEL OF GROWTH AND DISTRIBUTION

2016 ◽  
Vol 20 (7) ◽  
pp. 1934-1952 ◽  
Author(s):  
Kirill Borissov
Keyword(s):  
Economic Growth ◽  
Steady State ◽  
Simple Model ◽  
Disposable Income ◽  
State Equilibrium ◽  
Positional Concerns ◽  
The Poor ◽  
The Rich ◽  
Intertemporal Equilibrium ◽  
Unique Steady State

We consider a model of economic growth with altruistic agents who care about their consumption and the disposable income of their offspring. The agents' consumption and the offspring's disposable income are subject to positional concerns. We show that, if the measure of consumption-related positional concerns is sufficiently low and/or the measure of offspring-related positional concerns is sufficiently high, then there is a unique steady-state equilibrium, which is characterized by perfect income and wealth equality, and all intertemporal equilibira converge to it. Otherwise, in steady-state equilibria, the population splits into two classes, the rich and the poor; under this scenario, in any intertemporal equilibrium, all capital is eventually owned by the households that were the wealthiest from the outset and all other households become poor.

Criteria for a unique steady state for enzymatic depectinization of bael (Aegle marmelos) juice in a continuous stirred tank reactor

2018 ◽  
Vol 3 (3) ◽  
pp. 333-343
Author(s):  
Sourav Sengupta ◽  
Amit Jain ◽  
Sirshendu De
Keyword(s):  
Steady State ◽  
Stirred Tank ◽  
Continuous Stirred Tank Reactor ◽  
Aegle Marmelos ◽  
Stirred Tank Reactor ◽  
Tank Reactor ◽  
Continuous Stirred Tank ◽  
Kinetics Of ◽  
Unique Steady State

The depectinization kinetics of bael (Aegle marmelos) juice using the enzyme pectinase was evaluated and it was observed to follow the Michaelis–Menten model.

scholarly journals Ribosome flow model with extended objects

2017 ◽  
Vol 14 (135) ◽  
pp. 20170128 ◽  
Author(s):  
Yoram Zarai ◽  
Michael Margaliot ◽  
Tamir Tuller
Keyword(s):  
Steady State ◽  
Production Rate ◽  
Protein Production ◽  
Flow Model ◽  
Mean Field ◽  
State Density ◽  
Transition Rates ◽  
Ribosome Density ◽  
Protein Production Rate ◽  
Unique Steady State

We study a deterministic mechanistic model for the flow of ribosomes along the mRNA molecule, called the ribosome flow model with extended objects  (RFMEO). This model encapsulates many realistic features of translation including non-homogeneous transition rates along mRNA, the fact that every ribosome covers several codons, and the fact that ribosomes cannot overtake one another. The RFMEO is a mean-field approximation of an important model from statistical mechanics called the totally asymmetric simple exclusion process with extended objects (TASEPEO). We demonstrate that the RFMEO describes biophysical aspects of translation better than previous mean-field approximations, and that its predictions correlate well with those of TASEPEO. However, unlike TASEPEO, the RFMEO is amenable to rigorous analysis using tools from systems and control theory. We show that the ribosome density profile along the mRNA in the RFMEO converges to a unique steady-state density that depends on the length of the mRNA, the transition rates along it, and the number of codons covered by every ribosome, but not on the initial density of ribosomes along the mRNA. In particular, the protein production rate also converges to a unique steady state. Furthermore, if the transition rates along the mRNA are periodic with a common period  T then the ribosome density along the mRNA and the protein production rate converge to a unique periodic pattern with period  T , that is, the model entrains to periodic excitations in the transition rates. Analysis and simulations of the RFMEO demonstrate several counterintuitive results. For example, increasing the ribosome footprint may sometimes lead to an increase in the production rate. Also, for large values of the footprint the steady-state density along the mRNA may be quite complex (e.g. with quasi-periodic patterns) even for relatively simple (and non-periodic) transition rates along the mRNA. This implies that inferring the transition rates from the ribosome density may be non-trivial. We believe that the RFMEO could be useful for modelling, understanding and re-engineering translation as well as other important biological processes.

Newtonian repulsion and radial confinement: Convergence toward steady state

2021 ◽  
pp. 1-25
Author(s):  
Ruiwen Shu ◽  
Eitan Tadmor
Keyword(s):  
Steady State ◽  
Decay Rate ◽  
Large Time ◽  
Large Time Behavior ◽  
Steady States ◽  
Parameter Family ◽  
Time Behavior ◽  
Comparison Argument ◽  
Algebraic Convergence ◽  
Unique Steady State

We investigate the large time behavior of multi-dimensional aggregation equations driven by Newtonian repulsion, and balanced by radial attraction and confinement. In case of Newton repulsion with radial confinement we quantify the algebraic convergence decay rate toward the unique steady state. To this end, we identify a one-parameter family of radial steady states, and prove dimension-dependent decay rate in energy and 2-Wassertein distance, using a comparison with properly selected radial steady states. We also study Newtonian repulsion and radial attraction. When the attraction potential is quadratic it is known to coincide with quadratic confinement. Here, we study the case of perturbed radial quadratic attraction, proving that it still leads to one-parameter family of unique steady states. It is expected that this family to serve for a corresponding comparison argument which yields algebraic convergence toward steady repulsive-attractive solutions.

scholarly journals Ribosome flow model with positive feedback

2013 ◽  
Vol 10 (85) ◽  
pp. 20130267 ◽  
Author(s):  
Michael Margaliot ◽  
Tamir Tuller
Keyword(s):  
Steady State ◽  
Equilibrium Point ◽  
Positive Feedback ◽  
Flow Model ◽  
Linear Feedback ◽  
Model Parameters ◽  
Stable Equilibrium Point ◽  
Initiation Rate ◽  
Translation Rate ◽  
Unique Steady State

Eukaryotic mRNAs usually form a circular structure; thus, ribosomes that terminatae translation at the 3′ end can diffuse with increased probability to the 5′ end of the transcript, initiating another cycle of translation. This phenomenon describes ribosomal flow with positive feedback—an increase in the flow of ribosomes terminating translating the open reading frame increases the ribosomal initiation rate. The aim of this paper is to model and rigorously analyse translation with feedback. We suggest a modified version of the ribosome flow model, called the ribosome flow model with input and output . In this model, the input is the initiation rate and the output is the translation rate. We analyse this model after closing the loop with a positive linear feedback. We show that the closed-loop system admits a unique globally asymptotically stable equilibrium point. From a biophysical point of view, this means that there exists a unique steady state of ribosome distributions along the mRNA, and thus a unique steady-state translation rate. The solution from any initial distribution will converge to this steady state. The steady-state distribution demonstrates a decrease in ribosome density along the coding sequence. For the case of constant elongation rates, we obtain expressions relating the model parameters to the equilibrium point. These results may perhaps be used to re-engineer the biological system in order to obtain a desired translation rate.

scholarly journals State Trajectories Analysis for a Class of Tubular Reactor Nonlinear Nonautonomous Models

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
B. Aylaj ◽  
M. E. Achhab ◽  
M. Laabissi
Keyword(s):  
Steady State ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Tubular Reactor ◽  
Unique Steady State

The existence and uniqueness of global mild solutions are proven for a class of semilinear nonautonomous evolution equations. Moreover, it is shown that the system, under considerations, has a unique steady state. This analysis uses, essentially, the dissipativity, a subtangential condition, and the positivity of the relatedC0-semigroup.

Thermal runaway in a non-local problem modelling Ohmic heating. Part II: General proof of blow-up and asymptotics of runaway

1995 ◽  
Vol 6 (3) ◽  
pp. 201-224 ◽  
Author(s):  
A. A. Lacey
Keyword(s):  
Steady State ◽  
Blow Up ◽  
Ohmic Heating ◽  
Local Problem ◽  
Asymptotically Stable ◽  
Local Behaviour ◽  
Globally Asymptotically Stable ◽  
Non Local ◽  
Image Position ◽  
Unique Steady State

We consider the non-local problemIt is found that for the case of decreasingfthen: (i) forthere is a unique steady state which is globally asymptotically stable; (ii) forthen the problem can be scaled so thatin which case: (a) for λ < 8 there is a unique steady state which is globally asymptotically stable; (b) for λ = 8 there is no steady state anduis unbounded; (c) for λ > 8 there is no steady state andublows up for allx, −1 <x, < 1. Some formal asymptotic estimates for the local behaviour ofuas it blows up are obtained.

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