scholarly journals Representation of Kinetics Models in Batch Flotation as Distributed First-Order Reactions

Minerals ◽  
2020 ◽  
Vol 10 (10) ◽  
pp. 913
Author(s):  
Luis Vinnett ◽  
Kristian E. Waters
Keyword(s):  
Domain Model ◽  
Shape Parameters ◽  
First Order ◽  
Fractional Kinetics ◽  
Reaction Orders ◽  
Order Representation ◽  
Original Domain ◽  
S Model ◽  
Stretched Exponentials ◽  
Order Domain

Four kinetic models are studied as first-order reactions with flotation rate distribution f(k): (i) deterministic nth-order reaction, (ii) second-order with Rectangular f(k), (iii) Rosin–Rammler, and (iv) Fractional kinetics. These models are studied because they are considered as alternatives to the first-order reactions. The first-order representation leads to the same recovery R(t) as in the original domain. The first-order R∞-f(k) are obtained by inspection of the R(t) formulae or by inverse Laplace Transforms. The reaction orders of model (i) are related to the shape parameters of first-order Gamma f(k)s. Higher reaction orders imply rate concentrations at k ≈ 0 in the first-order domain. Model (ii) shows reverse J-shaped first-order f(k)s. Model (iii) under stretched exponentials presents mounded first-order f(k)s, whereas model (iv) with derivative orders lower than 1 shows from reverse J-shaped to mounded first-order f(k)s. Kinetic descriptions that lead to the same R(t) cannot be differentiated between each other. However, the first-order f(k)s can be studied in a comparable domain.

scholarly journals First-order discrete Faddeev gravity at strongly varying fields

2017 ◽  
Vol 32 (35) ◽  
pp. 1750181
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
Dimensional Space ◽  
Tetrad Field ◽  
First Order ◽  
Antiferromagnetic Structure ◽  
Riemannian Connection ◽  
Order Representation ◽  
Independent Variable ◽  
The Continuum ◽  
Elementary Area ◽  
Classical Background

We consider the Faddeev formulation of general relativity (GR), which can be characterized by a kind of d-dimensional tetrad (typically d = 10) and a non-Riemannian connection. This theory is invariant w.r.t. the global, but not local, rotations in the d-dimensional space. There can be configurations with a smooth or flat metric, but with the tetrad that changes abruptly at small distances, a kind of “antiferromagnetic” structure. Previously, we discussed a first-order representation for the Faddeev gravity, which uses the orthogonal connection in the d-dimensional space as an independent variable. Using the discrete form of this formulation, we considered the spectrum of (elementary) area. This spectrum turns out to be physically reasonable just on a classical background with large connection like rotations by [Formula: see text], that is, with such an “antiferromagnetic” structure. In the discrete first-order Faddeev gravity, we consider such a structure with periodic cells and large connection and strongly changing tetrad field inside the cell. We show that this system in the continuum limit reduces to a generalization of the Faddeev system. The action is a sum of related actions of the Faddeev type and is still reduced to the GR action.

General models for r-molecular reactions

1969 ◽  
Vol 6 (1) ◽  
pp. 74-87 ◽  
Author(s):  
G.M. Tallis ◽  
R.T. Leslie
Keyword(s):  
Stochastic Models ◽  
Diffusion Theory ◽  
First Passage Time ◽  
Passage Time ◽  
Theory Approach ◽  
Deterministic Theory ◽  
First Order ◽  
Time Problem ◽  
Reaction Orders ◽  
First Passage Time Problem

In the present paper we consider the r-molecular reversible reaction rA⇌B from several viewpoints. The deterministic theory for integral reaction orders is considered first and is subsequently extended to cover the case of fractional order reactions. Stochastic models are then proposed, the analyses being carried through by spectral methods and, in the case of first order reactions, the first passage time problem is also examined. Finally, we use a diffusion theory approach to the problem to obtain results which are valid for a large number of molecules.

scholarly journals On the State Approach Representations of Convolutional Codes over Rings of Modular Integers

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2962
Author(s):  
Ángel Luis Muñoz Muñoz Castañeda ◽  
Noemí DeCastro-García ◽  
Miguel V. Carriegos
Keyword(s):  
Coding Theory ◽  
Convolutional Codes ◽  
Codes Over Rings ◽  
Input State ◽  
First Order ◽  
Convolutional Coding ◽  
Artinian Rings ◽  
Base Ring ◽  
Order Representation ◽  
Classical Construction

In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base ring is local. When the base ring is a finite field, we recover the classical construction, studied in depth by J. Rosenthal and E. V. York. This allows us to construct observable convolutional codes over such rings in the same way as is carried out in classical convolutional coding theory. Furthermore, we prove the minimality of the obtained representations. This completes the study of the existence of input/state/output representations of convolutional codes over rings of modular integers.

scholarly journals Generic Noninteger Order Controller for Time-Delay Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Sami Hafsi ◽  
Sadem Ghrab ◽  
Kaouther Laabidi
Keyword(s):  
Time Delay ◽  
Stability Region ◽  
Delay Systems ◽  
Pid Controllers ◽  
Time Delay Systems ◽  
First Order ◽  
Industrial Utilization ◽  
Complete Set ◽  
Order Representation ◽  
Fractional Controller

This paper focuses on the problem of fractional controller P I stabilization for a first-order time-delay systems. For this reason, we utilize the Hermite–Biehler and Pontryagin theorems to compute the complete set of the stabilizing P I λ parameters. The widespread industrial utilization of PID controllers and the potentiality of their noninteger order representation justify a timely interest in P I λ tuning techniques. Step responses are calculated through K p , K i , l a m b d a parameters inside and outside stability region to prove the method efficiency.

KINETICS OF CATALYTIC REACTIONS ON A UNIFORM SURFACE AND SINGLE SITES: SIMILARITY AND DIFFERENCE

2009 ◽  
Vol 16 (05) ◽  
pp. 757-760 ◽  
Author(s):  
VLADIMIR P. ZHDANOV
Keyword(s):  
Reaction Scheme ◽  
Catalytic Reactions ◽  
First Order ◽  
Metal Atoms ◽  
Catalytic Sites ◽  
Reaction Orders ◽  
Similarities And Differences ◽  
Similarity And Difference ◽  
Kinetics Of ◽  
Kinetics Of Catalytic Reactions

To illustrate typical similarities and differences in the reaction kinetics occurring on a uniform surface and single sites (e.g. on single metal atoms incorporated into the inner walls of zeolite), we analyze a generic reaction scheme of N2O decomposition running in the presence of oxygen. In both cases, there are three reaction regimes, (i) controlled exclusively by the N2O -decomposition step, (ii) partly inhibited by oxygen, or (iii) limited by oxygen desorption. Regime (i) is kinetically similar (first order in N2O ) in the two cases. The states of the catalytic sites are however different. Regime (ii) exhibits different reaction orders in oxygen (-0.5 for the surface and -1 for single sites). Regime (iii) is fully identical in both the cases.

ON THE GENERAL INTERPRETATION OF FIRST-ORDER QUANTIFIERS

2013 ◽  
Vol 6 (4) ◽  
pp. 637-658 ◽  
Author(s):  
G.ALDO ANTONELLI
Keyword(s):  
General Setting ◽  
Second Order ◽  
First Order ◽  
Power Set ◽  
Full Power ◽  
Order Domain

AbstractWhile second-order quantifiers have long been known to admit nonstandard, or“general” interpretations, first-order quantifiers (when properly viewed as predicates of predicates) also allow a kind of interpretation that does not presuppose the full power-set of that interpretation’s first-order domain. This paper explores some of the consequences of such “general” interpretations for (unary) first-order quantifiers in a general setting, emphasizing the effects of imposing various further constraints that the interpretation is to satisfy.

Calculation of Surface Deformation in Point Contact EHD

1977 ◽  
Vol 99 (3) ◽  
pp. 313-317 ◽  
Author(s):  
S. Biswas ◽  
R. W. Snidle
Keyword(s):  
Surface Deformation ◽  
Point Contact ◽  
Order Method ◽  
Point Contacts ◽  
Numerical Techniques ◽  
Accurate Evaluation ◽  
First Order ◽  
Order Representation ◽  
Triangular Elements ◽  
Better Than

The paper describes three different numerical techniques for the accurate evaluation of the elastic deformation in elastohydrodynamic point contacts. The first method relies on a first order representation of the pressure distribution over triangular elements whereas the second and third methods use a second order method with rectangular elements. Comparison of results obtained using the numerical techniques described with known, exact values indicates that accuracies better than one percent can be expected when using the methods in the ehd problem.

Sign in / Sign up

Export Citation Format

Share Document