ON STABILITY OF STATIONARY STATES OF REVERSIBLE REACTIONS OF THE FIRST ORDER

The article discusses reversible first-order reactions. A system of differential equations is written. First integral and stationary state found. Using Lyapunov's direct method, stationary stability was investigated

Lack of Plasma-like Screening Mechanism in Sedimentation of a Non-Brownian Suspension

We investigate qualitatively a uniform non-Brownian sedimenting suspension in a stationary state. As a base of our analysis we take the BBGKY hierarchy derived from the Liouville equation. We then show that assumption of the plasma-like screening relations can cancel some long-range terms in the hierarchy but it does not provide integrable solutions for correlation functions. This suggests breaking the translational symmetry of the system. Therefore a non-uniform structure can develop to suppress velocity fluctuations and make the range of correlations finite.

The Limitation of the Combination of Transition State Theory and Thermodynamics for the Reactions of Proteins and Nucleic Acids

When a reaction is accompanied by a change with the speed close to or slower than the reaction rate, a circulating reaction flow can exist among the reaction states in the macroscopic stationary state. If the accompanying change were at equilibrium in the timescale of the relevant reaction, the transition-state theory would hold to eliminate the flow.

Utopia?

The final chapter takes up the charge that the program envisaged is a utopian fantasy. Could the Deweyan society be achieved? If it were achieved, could it be sustained? Both questions are addressed. The seven characteristic features of the Deweyan society depend on a systematic change: once a society has reached a stage of economic comfort, it can increase the time spent away from the workplace instead of striving for ever greater productivity. The crucial move in bringing about the Deweyan society is to declare that enough is enough. The bulk of the subsequent discussion attempts to demonstrate that forgoing productivity needn’t spell economic (or social) doom. It concludes with some clarifications of the thesis that markets are essential to economic health, and with a defense of John Stuart Mill’s claim that the “stationary state” is not something to be feared, but, quite possibly, an enormous improvement on the way people currently live.

Explosive Behaviors on Coupled Fractional-Order System

Fractional derivatives provide a prominent platform for various chemical and physical system with memory and hereditary properties, while most of the previous differential systems used to describe dynamic phenomena including oscillation quenching are integer order. Here, effects of fractional derivative on the transition process from oscillatory state to stationary state are illustrated for the first time on mean-filed coupled oscillators. It is found the fractional derivative could induce the emergence of a first-order discrete transition with hysteresis between oscillatory and stationary state. However, if the fractional derivative is smaller than the critical value, the transition will be invertible. Besides, the theoretical conditions for the steady state are calculated via Lyapunov indirect method which probe that, the backward transition point is unrelated to mean-field density. Our result is a step forward in enlightening the control mechanism of explosive phenomenon, which is of great importance to highlight the function of fractional-order derivative in the emergence of collective behaviors on coupled nonlinear model.

Dynamic Self-organization in an Open Reaction Network as a Fundamental Mechanism for the Emergence of Life

<p>The emergence of life on the earth has attracted intense attention but still remained an unsolved question. A key problem is that it has been left unclear why a living organism can have self-organizing ability leading to highly ordered structures and evolutionary behavior. This work reveals by computer simulation and experiments that a stationary state of an open reaction network, into which some source substances flow at constant rates, really has such self-organizing ability. The point is that reaction and diffusion processes in an open reaction network are irreversible and always forced to approach equilibrium. Therefore, they necessarily reach a stationary state in which they approach equilibrium to the largest extent as a whole and attain a full balance. This means that a stationary state of an open reaction network is firmly stabilized by irreversible reaction and diffusion processes and kept stable against fluctuation, namely it has ability to organize itself. A stationary state of an open reaction network is also flexible in structure and can evolve based on its own self-organizing ability through interaction with the environment. Thus, this work provides a new general mechanism of self-organization and evolution in a prebiotic chemical system, which is expected to have acted as a fundamental principle for the emergence of life on the earth. It is interesting to note that a network of reversible processes in a machine has no self-organizing ability because a reversible process has no property of spontaneously and irreversibly happening in a particular direction. </p>

Controlling effort, catch and biomass in models of the global marine fisheries

The starting point is the reduced model of global marine fisheries designated by W-3. The main variables of an ordinary differential equation are: the stock of bioresource, its net natural increase, as well as the catch value, which linearly depends on exogenous effort and nonlinearly on available biomass. In W-4, the effort became endogenous as a result of its positive feedback from biomass. In both models, there are values of control parameters in the catch equations, in which the value of the latter can be maintained for a long time at the maximum stable level, with the exception of transition sections. The principle of necessary precaution is fulfilled for small fish stocks more reliably in W-4 than in W-3, thanks to the transformation of the saddle into an unstable node with a common stable node. For these one-dimensional models, the author proposed an original generalization - the R-1 model of two nonlinear ordinary differential equations. In the latter effort, a new phase variable appears, subordinated to proportional control and derivative regulation. Biomass serves as a “prey”, and the effort appears as a “predator”. For two key control parameters, areas of change were identified for which the target stationary state is a locally asymptotically stable node or focus in R-1. A policy has been proposed for the restoration of depleted fish stocks and a transition to a long-term maximum sustainable harvest has been determined. Optimization over a wide time frame (from 40 to 400 years) allows us to calculate the values of the selected control parameters for which the integral catch volume in R-1 is higher than in W-4 for the same initial values of stock, effort and catch. Social constraints from below on the magnitude of the effort, as well as the desired nature of the transition to the target stationary state, are taken into account. The danger of biomass collapse is overcome, unlike previous models.

Relaxation Dynamics of Point Vortices

We study a model describing relaxation dynamics of point vortices, from quasi-stationary state to the stationary state. It takes the form of a mean field equation of Brownian point vortices derived from Chavanis, and is formulated by our previous work as a limit equation of the patch model studied by Robert-Someria. This model is subject to the micro-canonical statistic laws; conservation of energy, that of mass, and increasing of the entropy. We study the existence and nonexistence of the global-in-time solution. It is known that this profile is controlled by a bound of the negative inverse temperature. Here we prove a rigorous result for radially symmetric case. Hence E/M2 large and small imply the global-in-time and blowup in finite time of the solution, respectively. Where E and M denote the total energy and the total mass, respectively.

Power law distributions in a new toy model with interacting N agents

A new toy model with interacting N agents is proposed in this paper. The agents in this model possess quantity, and have an interaction radius depending on the quantity. They exchange a part of the quantity with agents belonging to within their interaction radii. The cumulative distribution function about observing the quantity in a stationary state exhibits a power law, and the exponent is universally close to –1 if the density of agents is sufficiently small.