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The radiative flux and heat flux are specific cases of energy flux. Particle flux, the rate of transfer of particles through a unit area (number of particles m −2 s −1 ) These fluxes are vectors at each point in space, and have a definite magnitude and direction. Since 2007, FLUX:: creates intuitive and technically innovative audio software tools, used by sound engineers and producers in the music, broadcast, post production, mastering.

6.3 Explaining Gauss's Law

5. Two concentric spherical surfaces enclose a point charge q. The radius of the outer sphere is twice that of the inner one. Compare the electric fluxes crossing the two surfaces.

6. Compare the electric flux through the surface of a cube of side length a that has a charge q at its center to the flux through a spherical surface of radius a with a charge q at its center.

7. (a) If the electric flux through a closed surface is zero, is the electric field necessarily zero at all points on the surface?

(b) What is the net charge inside the surface?

8. Discuss how Gauss's law would be affected if the electric field of a point charge did not vary as (displaystyle 1/r^2).

9. Discuss the similarities and differences between the gravitational field of a point mass m and the electric field of a point charge q.

10. Discuss whether Gauss's law can be applied to other forces, and if so, which ones.

11. Is the term (displaystyle vec{E}) in Gauss's law the electric field produced by just the charge inside the Gaussian surface?

12. Reformulate Gauss's law by choosing the unit normal of the Gaussian surface to be the one directed inward.

Simulations using flux balance analysis can be solved usingModel.optimize(). This will maximize or minimize (maximizing is thedefault) flux through the objective reactions.

4.1. Running FBA¶

The Model.optimize() function will return a Solution object. A solutionobject has several attributes:

• objective_value: the objective value
• status: the status from the linear programming solver
• fluxes: a pandas series with flux indexed by reaction identifier.The flux for a reaction variable is the difference of the primalvalues for the forward and reverse reaction variables.
• shadow_prices: a pandas series with shadow price indexed by themetabolite identifier.

For example, after the last call to model.optimize(), if theoptimization succeeds it's status will be optimal. In case the model isinfeasible an error is raised.

The solvers that can be used with cobrapy are so fast that for manysmall to mid-size models computing the solution can be even faster thanit takes to collect the values from the solver and convert to thempython objects. With model.optimize, we gather values for allreactions and metabolites and that can take a significant amount of timeif done repeatedly. If we are only interested in the flux value of asingle reaction or the objective, it is faster to instead usemodel.slim_optimize which only does the optimization and returns theobjective value leaving it up to you to fetch other values that you mayneed.

4.1.1. Analyzing FBA solutions¶

Models solved using FBA can be further analyzed by using summarymethods, which output printed text to give a quick representation ofmodel behavior. Photo mechanic 6 0 build 3143 download free. Calling the summary method on the entire model displaysinformation on the input and output behavior of the model, along withthe optimized objective.

In addition, the input-output behavior of individual metabolites canalso be inspected using summary methods. For instance, the followingcommands can be used to examine the overall redox balance of the model

Or to get a sense of the main energy production and consumptionreactions

4.2. Changing the Objectives¶

The objective function is determined from the objective_coefficientattribute of the objective reaction(s). Generally, a 'biomass' functionwhich describes the composition of metabolites which make up a cell isused.

Currently in the model, there is only one reaction in the objective (thebiomass reaction), with an linear coefficient of 1.

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The objective function can be changed by assigning Model.objective,which can be a reaction object (or just it's name), or a dict of{Reaction:objective_coefficient}.

We can also have more complicated objectives including quadratic terms.

4.3. Running FVA¶

FBA will not give always give unique solution, because multiple fluxstates can achieve the same optimum. FVA (or flux variability analysis)finds the ranges of each metabolic flux at the optimum.

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Setting parameter fraction_of_optimium=0.90 would give the fluxranges for reactions at 90% optimality.

The standard FVA may contain loops, i.e. high absolute flux values thatonly can be high if they are allowed to participate in loops (amathematical artifact that cannot happen in vivo). Use the looplessargument to avoid such loops. Below, we can see that FRD7 and SUCDireactions can participate in loops but that this is avoided when usingthe looplesss FVA.

4.3.1. Running FVA in summary methods¶

Flux variability analysis can also be embedded in calls to summarymethods. For instance, the expected variability in substrate consumptionand product formation can be quickly found by

Similarly, variability in metabolite mass balances can also be checkedwith flux variability analysis.

In these summary methods, the values are reported as a the center point+/- the range of the FVA solution, calculated from the maximum andminimum values.

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4.4. Running pFBA¶

Parsimonious FBA (often written pFBA) finds a flux distribution whichgives the optimal growth rate, but minimizes the total sum of flux. Thisinvolves solving two sequential linear programs, but is handledtransparently by cobrapy. For more details on pFBA, please see Lewis etal. (2010).

These functions should give approximately the same objective value.

4.5. Running geometric FBA¶

Geometric FBA finds a unique optimal flux distribution which is centralto the range of possible fluxes. For more details on geometric FBA,please see K Smallbone, E Simeonidis(2009).

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In these summary methods, the values are reported as a the center point+/- the range of the FVA solution, calculated from the maximum andminimum values.

Flux 7 7 0 8 Meters

4.4. Running pFBA¶

Parsimonious FBA (often written pFBA) finds a flux distribution whichgives the optimal growth rate, but minimizes the total sum of flux. Thisinvolves solving two sequential linear programs, but is handledtransparently by cobrapy. For more details on pFBA, please see Lewis etal. (2010).

These functions should give approximately the same objective value.

4.5. Running geometric FBA¶

Geometric FBA finds a unique optimal flux distribution which is centralto the range of possible fluxes. For more details on geometric FBA,please see K Smallbone, E Simeonidis(2009).

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