Fisher equation

This is sometimes known as the cubic Fisher equation and has been applied variously in chemical kinetics, population biology, and to the spread of infectious diseases or advantageous genes. 

The evaluation of stability for travelling-wave solutions is by no means a simple process and will not even be attempted here. The result that systems governed by quadratic Fisher equations tend to pick up their minimum permitted velocity will be used later. 

This is a cubic Fisher equation. The final term corresponds to the chemical kinetics, and we need to establish when this term becomes zero. One solution is / = 0, which matches the boundary condition as z -> + oo. The other two zeros in the kinetic term arise when... 

As a canonical model representing the reaction A + B —> 2B (see Sect. 3.1.3) we consider the Fisher equation (4.16) with advection (Neufeld et ah, 2002b)... 

Source Advances in Chemistry Series, no. 22, Physical Properties of Chemical Compounds, vol. II (Washington, DC American Chemical Society, 1959) and C. H. Fisher, Equations Correlate n-Alkane Physical Properties with Chain Length, Chemical Engineering, September 20 111-113 (1982). 

C. H. Fisher, Equations Correlate n-Alkane Physical Properties with Chain Length, Chemical Engineering, September 20 111-113 (1982). 

The influence of PMMA content on the kinetic and thermodynamic parameters controlling the isothermal spherulitic growth and the overall crystallization rate of PEG from the molten blends has been analyzed on the basis of the modified Tumbul 1-Fisher equation ... 

The Fisher equation, which predated the existence of inflation-linked bond markets, states that a nominal bond yield is made up of three components—inflationary expectations, a required real yield that investors demand over and above those inflationary expectations, and a risk premium. The risk premium reflects the assumption that investors want additional compensation for accepting undesirable inflation risk when holding (therefore suboptimal) nominal bonds. 

On this basis, there is a huge urge to say you can t do it, but we must try to offer something a little more constructive. Nobody ever asks what the duration of an equity is, but the question is almost equivalent—linkers, like equities, are a different asset class. There are equity duration measurements—price sensitivities with respect to changes in the earnings yield or dividend yield—and equities can be related to nominal bonds via a Fisher equation as we have shown, just as linkers are related to nominals via a Fisher equation. However, equity duration numbers are seldom calculated, and would never be used in a mixed portfolio of equities and bonds to give a total portfolio duration. 

If we think about the simplified Fisher equation for linkers. 

The only mathematically correct way to report duration for a mixed portfolio of nominals and linkers, in a way that adds some useful information, is to drop the standard duration figure and instead show two new numbers duration with respect to real yield and duration with respect to inflationary expectations. These are the two main partial derivatives of the Fisher equation. 

To see why, let s reduce the Fisher equation to the more manageable form ... 

Investors who are long-familiar with nominal bonds should probably not even ask the question, thinking back to the Fisher equation. If they... 

Fisher—he of the famous Fisher equation—argued that the real yield should be constant. However, the evidence to support this much less well-known hypothesis is patchy to say the least. 

Almost parallel to McKendrick, Hutchinson [215], a well-known ecologist, proposed a time-delayed version for the logistic growth equation, where the nonlinear term was delayed in time. The diffusive Hutchinson equation, also known as the delayed Fisher equation. 

The integrand is appreciably different from zero only in the front region of the wave a smaller value of v corresponds to a narrower, i.e., steeper front. As for the Fisher equation (4.1), the steepness of the wave front depends inversely on the wave velocity V, and natural initial conditions, i.e., initial conditions that are localized or that decay faster than exponentially, relax to the front with the minimal front velocity. The minimal front velocity for the Fisher DIRW is smaller than the minimal front velocity for the Fisher equation, prd = 2 /d, see Sect. 4.1.1, and approaches the latter in the diffusive limit. 

Fig. 7.11 Plot of the results for the front velocity vs the parameter rr. The points tire obttiined from simulations of the stochastic process on the OCNs (fiill circles) tmd the Peano basin open circles). The lines correspond to theoretical values from the Fisher equation (solid) and for the Peano basin (dotted and dotted-dashed). Reprinted from [64]. Copyright 2006, with permission from Elsevier...

Some authors used subsolutions, supersolutions, and comparison theorems to analyze the stability of the nontrivial steady state "pix) [257]. For the Fisher equation, Skellam s linear stability analysis about p(x) can be used [414]. If we set p x, t) = p x) + hp(x, t) and consider the linearization of (9.1) about p(x), we obtain... 

Fedotov, S. Nonumfoim reaction rate distribution for the generalized Fisher equation ignition ahead of the reaction front. Phys. Rev. E 60(4), 4958-4961 (1999). http //dx.doi. org/10.1103/PhysRevE.60.4958... 

Gi Undisturbed spherulite growth rate of the homopolymer described by the Tumbull-Fisher equation... 

The authors gained two useful pieces of information from these fronts. First, they found that the velocity could be described by the Fisher equation (Fisher, 1937) ... 

Fisher, as well as other vendors, has equations for gas, vapour and steam flow which have two parameters. One parameter represents flow capacity and the other parameter represents the type of valve and its effect on critical flow. The Fisher equations are as follows ... 

---