scholarly journals Detailed balance for diffusion in a potential with trapping and forward–backward symmetry of trapping time distributions

2020 ◽  
Vol 152 (22) ◽  
pp. 226101
Author(s):  
Alexander M. Berezhkovskii ◽  
Dmitrii E. Makarov
Keyword(s):  
Detailed Balance ◽  
Trapping Time

Dielectronic Recombination in the Average-Atom Model

1988 ◽  
Vol 102 ◽  
pp. 215
Author(s):  
R.M. More ◽  
G.B. Zimmerman ◽  
Z. Zinamon
Keyword(s):  
Detailed Balance ◽  
Systematic Errors ◽  
Dielectronic Recombination ◽  
Rate Equations ◽  
Strong Correlations ◽  
Dense Plasmas ◽  
Atom Model ◽  
New Feature ◽  
Average Atom Model ◽  
Attachment Process

Autoionization and dielectronic attachment are usually omitted from rate equations for the non–LTE average–atom model, causing systematic errors in predicted ionization states and electronic populations for atoms in hot dense plasmas produced by laser irradiation of solid targets. We formulate a method by which dielectronic recombination can be included in average–atom calculations without conflict with the principle of detailed balance. The essential new feature in this extended average atom model is a treatment of strong correlations of electron populations induced by the dielectronic attachment process.

The Rotterdam Initiative in Reducing Waste Discharges at Source

1991 ◽  
Vol 24 (10) ◽  
pp. 171-177
Author(s):  
T. Vellinga ◽  
J. P. J. Nijssen
Keyword(s):  
Public Relations ◽  
Action Plan ◽  
Detailed Balance ◽  
River Rhine ◽  
The North ◽  
Complementary Role ◽  
Action Programme ◽  
The North Sea ◽  
Set Up

Much of the material dredged from the port of Rotterdam is contaminated to such a degree that it must be placed in specially constructed sites. The aim of Rotterdam is to ensure that the dredged material will once again be clean. This will entail the thorough cleansing of the sources of the contamination of the sediment in the harbours and in the River Rhine. The Rotterdam Rhine Research Project (RRP) is one of the means to achieve this based on: technical research, legal research, public relations and dialogues with dischargers. The programme for five selected heavy metals is almost complete. For many heavy metal discharge points between Rotterdam and Rheinfelden, a specially devised independent load assessment has been carried out four times. Balance studies were used to determine the relative contributions of the point discharges to the total. Currently the results are being used in an attempt to negotiate agreements with a selected number of the major dischargers. At present, more detailed balance studies are being set up and exploratory measurements carried out for organic micropollutants. It may be concluded that the research is progressing successfully and methods and techniques developed seem satisfactory and broadly applicable. The Rhine Action Programme encompasses an international effort to improve the quality of the Rhine water. Although the RRP plays a modest complementary role to the Rhine Action Plan, there is no doubt of the value of this Rotterdam initiative. The mode of work followed in the RRP contains elements that can be of use in combatting the contamination of the North Sea by rivers other than the Rhine.

scholarly journals Fast Reaction Limits via $$\Gamma $$-Convergence of the Flux Rate Functional

2021 ◽  
Author(s):  
Mark A. Peletier ◽  
D. R. Michiel Renger
Keyword(s):  
Evolution Equations ◽  
Detailed Balance ◽  
Approximate Solutions ◽  
Reaction Rates ◽  
Convergence Result ◽  
Rate Function ◽  
Jump Processes ◽  
Kolmogorov Equations ◽  
Markov Jump ◽  
Fast Reaction

AbstractWe study the convergence of a sequence of evolution equations for measures supported on the nodes of a graph. The evolution equations themselves can be interpreted as the forward Kolmogorov equations of Markov jump processes, or equivalently as the equations for the concentrations in a network of linear reactions. The jump rates or reaction rates are divided in two classes; ‘slow’ rates are constant, and ‘fast’ rates are scaled as $$1/\epsilon $$ 1 / ϵ , and we prove the convergence in the fast-reaction limit $$\epsilon \rightarrow 0$$ ϵ → 0 . We establish a $$\Gamma $$ Γ -convergence result for the rate functional in terms of both the concentration at each node and the flux over each edge (the level-2.5 rate function). The limiting system is again described by a functional, and characterises both fast and slow fluxes in the system. This method of proof has three advantages. First, no condition of detailed balance is required. Secondly, the formulation in terms of concentration and flux leads to a short and simple proof of the $$\Gamma $$ Γ -convergence; the price to pay is a more involved compactness proof. Finally, the method of proof deals with approximate solutions, for which the functional is not zero but small, without any changes.

Exact Stationary Response Solution for Second Order Nonlinear Systems Under Parametric and External White Noise Excitations: Part II

1988 ◽  
Vol 55 (3) ◽  
pp. 702-705 ◽  
Author(s):  
Y. K. Lin ◽  
Guoqiang Cai
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Probability Distribution ◽  
White Noise ◽  
Probability Density ◽  
Detailed Balance ◽  
Stationary Probability ◽  
Probability Flow ◽  
Parametric And External Excitations ◽  
White Noises

A systematic procedure is developed to obtain the stationary probability density for the response of a nonlinear system under parametric and external excitations of Gaussian white noises. The procedure is devised by separating the circulatory portion of the probability flow from the noncirculatory flow, thus obtaining two sets of equations that must be satisfied by the probability potential. It is shown that these equations are identical to two of the conditions established previously under the assumption of detailed balance; therefore, one remaining condition for detailed balance is superfluous. Three examples are given for illustration, one of which is capable of exhibiting limit cycle and bifurcation behaviors, while another is selected to show that two different systems under two differents sets of excitations may result in the same probability distribution for their responses.

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