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I have some mutants that have produced atypical melt curves via just standard DSF with Sypro orange then nanoDSF looking at intrinsic fluorescence. Ideas of further experiments that could be used to probe this further and elucidate details of stability and what's going on with these proteins?
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Dear @Gemma..
and what about the CBD? with sypro orange? Ir is show a normal slope?
From the 222 and CS6 spectra, that start with an high fluorescence alreraDY at low temperatures, it seems that your mutants are at least partially unfolded.
You can see an example of the DSF curve of a protein unfolded when trated with DTT at the minute 2:30 of the following video
pubblished on my blog, ProteoCool
I think that you can verify it in some alternative ways to confirm it:
1) check in SEC chromatography if they have different aggregation state
2) Run an 1D NMR spectra (unfolded proteins show lower peak dispertion)
3) Check the stability of the samples under concentration (If the protein is unfolded will tend to precipitate at lower concentration)
best regards
Manuele
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I am currently focusing on 3D geomechanical modeling. And in the future, I want to extend it to a 4D model. During my recent studies, I realized that most of the 4D geomechanical modeling that has been done has not properly updated the elastic properties such as Young's modulus, bulk modulus, Poisson ratio, etc. If a 3D static model is extended to a dynamic model, or a two-way or one-way coupling is performed, it is necessary to consider all material behaviors in a time-dependent manner. Please share if you have useful information in this regard or if you have a suggestion, I would be grateful if you could comment.
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Hi Erfan Rahimi , in time-dependent 3D geomechanical simulation ("4D" coupled flow and geomechanical simulations) there a many interdependencies between material properties (e.g., elastic properties, strength properties, porosity/ permeability, fluid properties) and simulated fields (stress, strain, pore pressure).
You have to think carefully when including additional interdependencies (or vice versa NOT including these interdependencies), whether they add (i) a lot of additional complexity, (ii) create a lot of additional insight, (iii) create complexity without creating insight, (iv) the error incurred by failing to include the interdependency. As you correctly point out, updating elastic properties in the overburden is NOT commonly for coupled flow and geomechanical modelling. This is one of the cases where you make the simulations a lot more complex, without adding a lot of insight. Elastic properties due to stress/strain changes in the overburden change by less than a percent from their initial value - and updating the elastic properties will affect the simulated stress field by an amount which is insignificant compared to our ability to calibrate the stress field. In your picture, you show a loop which includes updating of velocities for 4D seismic attribute generation. Here updating the velocities (even by less than 1%) results in something we can observe in field data in the form of time-lapse timeshifts. In a similar manner, if permeabilities are stress dependent in a significant manner and neglecting to include this coupling will create a large error, it is customary to include this coupling. Another example of coupling which is sometimes, but not always, used is to use non-linear stress-strain relationships in the reservoir, if significant compaction occurs and the reservoir rock will experience irreversible compaction.
In summary, keep models as simple as possible, and add complexity if there is a good reason. Do not fall into the trap of making models "complex" for the sake of complexity. Complex models are harder to interpret, and don't necessarily provide more insight. There is an unfortunate tendency of assuming that "complex" models are "better" models. They sometimes are, and often are not.
Hope this makes sense, and addresses your question.
Cheers,
Jorg
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Dear researchers
As we know, recently a new type of derivatives have been introduced which depend two parameters such as fractional order and fractal dimension. These derivatives are called fractal-fractional derivatives and divided into three categories with respect to kernel: power-law type kernel, exponential decay-type kernel, generalized Mittag-Leffler type kernel.
The power and accuracy of these operators in simulations have motivated many researchers for using them in modeling of different diseases and processes.
Is there any researchers working on these operators for working on equilibrium points, sensitivity analysis and local and global stability?
If you would like to collaborate with me, please contact me by the following:
Thank you very much.
Best regards
Sina Etemad, PhD
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Yes I am
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Hello, can someone help me in understanding how the variation in angle of attack effect the features of the transonic flow? I have read books on transonic flow, but they explain the effect of variation in mach number with transonic flow. How does tansonic features over a wing evolve with angle of attack ? What constitutes a good transonic wing ?
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Hello dear Vinay, in transonic flow we have a complex mixing of subsonic, sonic and weakly supersonic behaviour, angle of attack variation induces unstable choc waves in appearance and position, that create unsteady boundary layer separation.
the common soulution is to use supercritic airfoils, weakly curved in extrados and slightly more curved in intrados, that's divide strong choc wave in many little weaker choc waves with less noise effect.
I try to find you good references and book titles.
Good luck.
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Hello,
Would you have an idea on how to model stable regular networks in a phase field model ?
For instance a square network like in the joined picture (the picture was made artificially) ? I know that the Swift-Hohenberg equation allows to create some regularity but I would like to control more the size of the network and the distance between the branches, and maybe the type of network.
Thank you in advance :)
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I am looking for alkali stable radical scavengers.
I have a glycol solution of 80:20 ethyl diglycol:butyl glycol.
And want to add 10% KOH (so a waterless alkaline).
I have tried spiking the glycol solution with up to 2% BHT (butylated hydroxy toluene) before adding the KOH. As BHT is commonly used as antioxidant (radical scavenger)
However, it still seems unstable.
I was wondering if there are any Alkali stable radical scavengers or anything to supress discoloration and further (aldol) condensation of the present glycols.
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Dear researchers
As you know, nowadays optimal control is one of the important criteria in studying the qualitative properties of a given fractional dynamical system. What is the best source and paper for introducing optimal control analysis for fractional dynamical models?
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Dear Dr. @Muhammad Ali
Thank you very much.
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Any suggestions on analytical and numerical solutions? Any available codes to solve Mathieu equation available other than in math work websites ?
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The Mathieu equation has periodic solutions and therefore it is possible to use finite difference approximations to obtain an equivalent matrix eigenvalue problem. The matrix will of tridiagonal kind with an extra two coefficients, one top right and the other bottom left when second order accurate differences are used.
Also see:
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hello dear colleagues
I was working on a problem where I decide to merge sliding mode controller with homogeneous one. I was planning to define the sliding manifold based on homogeneous system of integrators.
Has anybody tried it out? are there any advantages?
best regards
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You are welcome. In my opinion, I think such papers have not yet been contributed, because the topic is brand-new and needs more research contributions to be recently developed. You may be the one who contributes the first paper on this field and with respect to the finite-time stabilization, compare such controllers together, in terms of advantages and disadvantages.
Regards
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I am trying to evaluate MWCNT nanofluid (NF) stability by measuring absorbance by UV vis, however since the concentration I am interested in leads to an opaque solution, I get absorbance higher than the max recommended for UV measurements (I get around 5). Is there is any why to come around this without changing concentration? , would decreasing cuvette path length solve the problem?
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@Muhammad Kaleem,
Many thanks for the spectra from the reference. It looks like their spectra from the films spun out from their solutions. Your spectra are from solutions. They should be different if it is true. You could measure the spectra from your thin fims from your solutions to compare with. This is also important information for your research too. Please make sure that you use UV grade substrates.
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concentration: 1and 2 %w
Solvent: deionized water
Storage time: 1 or a few days
Also a layer of mold can be see on it.
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Labile H are lost.
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The Van der Pol oscillator can be give in state model form as follows:
dx/dt = y
dy/dt = mu (1 - x^2) y - x,
where mu is a scalar parameter.
When mu = 0, the Van der Pol oscillator has simple harmonic motion. Its behavior is well-known.
When mu > 0, the Van der Pol oscillator has a stable limit cycle (with Hopf bifurcation).
While we can show the existence of a stable limit cycle with a MATLAB / SCILAB plot with some initial conditions and some positive value for mu like mu = 0.1 or 0.5 (for simulation), I like to know if there is a smart analytical proof (without any simulation) showing the existence of a limit cycle.
Specifically I like to know - is there any energy function V having time-derivative equal to zero along the trajectories of Van der Pol oscillator? Is there some smart calculation showing the existence of a stable limit cycle..
I am interested in knowing this - your help on my query is most welcome. Thanks!
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The following steps are helpful for finding the dynamics of the system:
1. Check the stability of equilibrium by the Jacobian method.
2. Find the parametric conditions of stability/unstability.
3. Check what type of Hopf bifurcation (subcritical/supercritical) is there.
4. If the Hopf bifurcation is supercritical, then there is a stable limit cycle.
5. You can also solve the system numerically in Matlab/Mathematica and plot the limit cycle.
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I have a real stable system. However, when I try to reconstruct the state-space matrices of my system by using the subspace identification, it resulted in an unstable A matrix where its eigenvalues are located outside the unit circle.
I know that there are some ways to forced the A matrix to be stable. But it tends to give us a biased result since the stability is forced, not naturally identify as a stable system.
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During the modeling process, it may be important to consider the relations of (input and output variables) , the governing differential modeling principles (including simplifications and linearity assumptions, steady-state conditions…), and after the model is obtained, see the properties of the eigenvalues of the system martrix (sign of roots, complex roots, if roots are bounded or not…), and or the poles of the transfer function T may be seen.
Given some system with matrix A find the characteristics polynomial of A.
Apply the “ Routh-Hurwitz” stability criterion on the polynomial.
(1) Negative eigenvalues lead to stable system
(2) Positive eigenvalues lead to unstable ones.
(3) Complex eigenvalues (may) tell us oscillatory conditions….
There may be other cases of considerations...
Thanks
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Please suggest if any specific software is used.
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I am in a holidays, away from the lab computer to check the options of origin, but anyane who have the experience in using it can provide help. Sorry for being unable to help at this time period.
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Hi everyone,
As known, the buoyancy frequency is defined as N^2=g/rho*drho/dz. Normally, the positive or negative characteristics of N^2 is the same as the gradient of water density (drho/dz), depended on the water temperature vertical profiles. In summer, the temperature of surface water is always higher than the lower zone, so drho/dz is positive. However, in autumn and winter, the surface temperature decreases, the temperature of surface water becomes lower than the lower zone, so drho/dz should be negative. The paradox is N^2 is a square number and should be always positive. I'd like to know how to explain such paradox of negative density gradient (drho/dz) and always positive buoyancy frequency (N^2)? Thanks a lot.
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Dear Pr. Carton,
Thank u very much for your clear answer, I understand your explanation well. In actuality, I am numerically solving a lake mixing model of methane, and I need to know the value of N2 to calculate the turbulence diffusivity (D), the equation as follows,
dC/dt = -Dd2C/dz2-r; r is the oxidation
In some articles, D is defined as D=8.94e-4[m^2/d]/(N2[1/s^2])^0.43. For this model, N2 cannot be a negative here. I don't know whether it is the problem of this model or sth. else. Thanks again.
Sincerely
Enze
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Hello
Why do we see the deposition of nanoparticles by adding different surfactants (cationic, anionic and non-ionic) with different concentrations to cobalt ferrite nanofluids?
Cobalt ferrite nanoparticles were synthesized by co-precipitation method.
Thank you all in advance
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I offer you our method for the synthesis of cobalt ferrite nanoparticles in a system of straight micelles. Its advantage: stability of dispersion, the formation of self-organized uniformly distributed nanoparticles as a result of a quantum-thermal phase transition.
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In the case of water splitting the water oxidation (OER) is the bottleneck for the process and because of the harsh conditions of the WO reaction, molecular catalysts with high TOFs are not stable in the matrix and quickly decompose. On the other hand heterogeneous catalysts are more stable but they often do not have high TOF quantities. Now what is your opinion about the future catalyst type? Will the ideal catalysts fabricated by turning the molecular catalysts to heterogeneous catalysts ( by loading the molecular catalysts on the solid surfaces ) or it will be from the single atom heterogeneous catalyst type?
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Dear Sina Safavi thank you for initiating this interesting RG discussion. Although we are inorganic chemists, I'm not an expert in this field. However, I agree with Yurii V Geletii in that there is no such thing as a true catalyst. In this context I suggest that you have a look at the following relevant article which has been published Open Access. It is stated there that future catalysts should be "low-cost and earth-abundant":
Earth-Abundant Electrocatalysts for Water Splitting: Current and Future Directions
(see attached pdf file)
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Hi! I am trying to find some studies (or be educated) on the stability of the following groups in highly acidic (pH ~ 1-3) aqueous solutions of either an oxidizing acid (sulfuric or nitric) or reducing acid (HBr):
-The urethane linkage itself
-Polycarbonate diol
-Polyacrylate (say, HEA or IBOA)
I have a UV curable coating with the above components (polyurethane prepolymer dissolved in an acrylate monomer) that will be exposed to various acidic solutions for up to 30 days at RT.
I am trying to determine where any reactions would take place and understand if the polymer would degrade. I don't think it will based off the backbone, but I am curious to learn the reasons why / why not.
Thanks!
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Dear Michael Bay, hydrolytic hydrolysis is the problem. To overcome this problem, superhydrophobic surfaces are the most followed solution. Please check the following documents. My Regards
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Dear all,
I am trying to couple a simulation with two codes, say code A and code B (different discretizations). For code A we solve simply the conduction equation (solid), while in B we solve the NS + temperature convection/diffusion (fluid).
The coupling is explicit, while the time scheme for each code is implicit.
at each iteration, code A gives code B the heat flux to impose at the boundary of domain B, while code B gives code A the temperature to impose at the boundary of domain A. So in short, the coupling is done via a Neumann/Dirichlet BCs.
I am facing stability issues that don't allow me to finish correctly the transient solution.
Let us focus only on domain A (code A). When code A receives the temperature values from code B to apply a Dirichlet BC, the values are stocked in a layer of cells; so called the ghost cells. We denote these values as T_wall.
Now, we need to compute the heat flux at the boundary to give to code B. There are two possibilities to compute such a flux :
1- use T_wall and one inner temperature value
2- use 2 or 3 inner temperature values to calculate the flux, and then extrapolate it to the boundary.
I am getting serious instabilities if I calculate the flux via the first approach (T_wall and 1 inner temperature value). Otherwise, with the second approach (only inner temperature values), the simulation is stable and a steady-state is reached.
Can I have please your opinion on this subject. Have you ever faced such kind of problems ?
Is it really that computing the flux with the second approach leads to a stable solution, but to a non-consevative scheme ?
Best regards
Elie Saikali
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Thanks for the answer and for the reference.
Regards
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I need to measure the CCT from rotor angle graph >> is it possible ? HOW?
it will be highly appreciated, if you advice any method to calculate the CCT
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This is a trial an error process in a multi.machine system, first of all you need to know a clearing time for a stable operating condition and another time for an unstable condition, then you can try another time from such an interval. Should the resulting condition is unstable you have to reduce the clearing time and run the simulation again, in this way you are reducing the interval until you reach the CCT
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I need guidance on the analytical model and calculation for shape (cross-section) optimization of Euler Bernoulli cantilever column under buckling with a point load. It may be using variational methods, with the use of Rayleigh Quotient.
For it, I found a similar case in "Haftka, Raphael & Gurdal, Zafer & Kamat, Manohar. Elements of structural optimization. 2nd revised ed." but with different boundary conditions, I have attached the scans of the procedure used in the text for reference.
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Dear all,
I am trying to couple a simulation with two codes, say code A and code B (different discretizations). For code A we solve simply the conduction equation (solid), while in B we solve the NS + temperature convection/diffusion (fluid).
The coupling is explicit, while the time scheme for each code is implicit.
at each iteration, code A gives code B the heat flux to impose at the boundary of domain B, while code B gives code A the temperature to impose at the boundary of domain A. So in short, the coupling is done via a Neumann/Dirichlet BCs.
I am facing stability issues that don't allow me to finish correctly the transient solution.
Let us focus only on domain A (code A). When code A receives the temperature values from code B to apply a Dirichlet BC, the values are stocked in a layer of cells; so called the ghost cells. We denote these values as T_wall.
Now, we need to compute the heat flux at the boundary to give to code B. There are two possibilities to compute such a flux :
1- use T_wall and one inner temperature value
2- use 2 or 3 inner temperature values to calculate the flux, and then extrapolate it to the boundary.
I am getting serious instabilities if I calculate the flux via the first approach (T_wall and 1 inner temperature value). Otherwise, with the second approach (only inner temperature values), the simulation is stable and a steady-state is reached.
Can I have please your opinion on this subject. Have you ever faced such kind of problems ?
Is it really true that computing the flux with the second approach leads to a stable solution, but to a non-consevative scheme ?
Best regards
Elie Saikali
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The stability condition is Fo Bi < 1 (CAST3M club presentation in 2019 at the CAST3M website by myself)... and serious references on the question :
Giles, M. B. "Stability analysis of numerical interface conditions in fluid–structure thermal analysis." International journal for numerical methods in fluids 25.4 (1997): 421-436.
Errera, Marc Paul, and Florent Duchaine, 2015. "STABLE AND FAST NUMERICAL SCHEMES FOR CONJUGATE HEAT TRANSFER."
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I have a question regarding STB in cadence should I set the operating point with STB analysis or not important? also, another question when I get the loop gain I found it below 0 dB what does it mean does that mean that there is no oscillation and the system is stable? … Read more
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Dear Hagar,
All you need is to apply the Barkhausen criterion” for sustained oscillations.
It is so that the negative feedback amplifier will be stable so long mag. AB is smaller at -180 degrees phase shift and it may oscillate if mag. AB is greater than one at -180 degrees phase shift.
Accordingly, so the amplifier at the top figure is stable. While it will be unstable in the bottom figure. The probable point of oscillations is slightly to the left of M2.
You can test the stability by an input impulse, if the amplifier is stable the impulse will decay and it will grow to grow if the amplifier is unstable.
This means that you let the amplifier function as an oscillator.
Yes what do you said is okay.
But I see in the top figure, the amplifier shows zero response at specific frequencies.
Best wishes
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I have the water dispersion of WO3 and Ni(OH)2. Both the dispersions containing 2D nanosheets are stable for more than a month. Dispersions of the bulk materials are not stable though. There are no other additives/surfactants in the dispersion. Measured Zeta potential value is -2mV. How the dispersion is stable then? Is it because of the less mass of the nanosheet compared to bulk Or any other reason?
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I do not believe you measured zeta potential (ZP) but some other property (e.g. electrophoretic or acoustic mobility) and you are using some/many assumptions in a conversion to ZP. This distinction is important because at higher concentrations, you will have particle-particle interactions and hence reduced mobility (which may be 'transformed' to a 'ZP' closer to 0 mV).
Why do you believe that ZP is a measure of 'stability'? [Whatever you mean by that] -echoing the comments of John Francis Miller .
Stability is conferred through charge (erroneously called electrostatic) or steric means. ZP is irrelevant to steric stability as the slipping plane is in the protective polymer 'coat'. Both stabilization mechanisms involve additives or change in pH. Hence DI water is about the worst material to dilute any system as it washes out/dilutes any stabilizing agents. The 'mother liquor' is the correct dilution medium.
Your comment 'bulk material is heavy and has higher chance of aggregation' is completely illogical. A density difference corresponds to settling propensity.
Pedantically I also cannot understand 'Dispersions of the bulk materials are not stable though. There are no other additives/surfactants in the dispersion. Measured Zeta potential value is -2mV'. You talk of 'dispersions' and 'bulk materials' (both plural) yet only have one single 'zeta potential' measurement (- 2 mV) - without indicating pH or other important parameters such as concentration. I would expect many 'ZP' measurements.
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We know that these elements are non-carbide formers. Therefore, C is more likely to be present in the solution which should make the austenite more stable. By this logic, adding these elements should make austenite stable up to an even lower temperature.
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Dear Arka,
Good afternoon!
I always try to keep in mind that C is an interstitial alloying element while Al, Co and Si are substitutional alloying elements n Fe based alloys (like steels).
That means that Al, Co and Si will "take the place" of Fe atoms in the crystals, differently than C, B and N that will be in the interstitial positions in both austenite and ferrite crystals...
In Fe alloys there are only 4 gammagenic alloying elements, as follows: Ni, Mn, C and N. These 4 chemical elements are, ALWAYS, austenite formers in Fe alloys.
Si is a strong alphagenic element. It means it is a ferrite former.
I would as well keep in mind that both Al and Si have strong affinity with oxygen, been considered deoxidant elements in Fe based alloys.
What I can guarantee to you is that Co will always shift the TTT curve to the left... But I do not agree that Al and Si will do the same.
Co is a very interesting alloying element in Fe alloys. Keep in mind that Co is neighbour of Fe in the periodic table! I would tell you that the important effect of reduction of stacking-fault energy (SFE) that Co creates in Fe based alloys may be the answer to this particular effect that Co will always shift the TTT curve to the left... But it is something that is not 100% explained yet.
Very interesting question... Thank you!
I hope to help you. If it makes sense to you, I invite you to read some of my papers...
And join our research team! You are very welcome!
André
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I am still unsure about the relationship between BIBO and Lyapunov stability of simple undelayed LTI SISO systems.
Basic facts:
1) The system is STABLE if it has all system poles (eigenvalues) in the open left-half plane (LHP) or even single poles on the imaginary axis.
2) The system is ASYMPTOTICALLY or EXPONENTIALLY STABLE if it has all system poles (eigenvalues) in the open left-half plane (LHP).
3) The system is BIBO STABLE if it has all system poles (eigenvalues) in the open left-half plane. Or, the system is BIBO STABLE if its impulse function is absolutely integrable (i.e., it is L1-stable).
4) Btw., it is a fact that LTI SISO systems with DELAYS can have infinitely many poles in the LHP except for the complex infinity. Such systems are EXPONENTIALLY stable but they can/cannot be ASYMPTOTICALLY, Hinf or BIBO stable. Here, moreover, BIBO implies Hinf stability.
Notes:
- Some authors consider BIBO stability as a feature of the TRANSFER FUNCTION, not the SYSTEM itself. That is, there may exist unstable modes that cannot be seen at the output in the system. Therefore, every asymptotically Lyapunov stable system is BIBO, not vice-versa.
- I found also the idea in the literature that BIBO is stronger than asymptotical Lyapunov stability – however, I mean that this is incorrect.
Could anyone clearly explain me whether it exist any general relationship (inclusion, implication,…) between BIBO and (asymptotic) Lyapunov stability for SISO LTI delay-free systems, please?
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Dear Libor,
I don’t know if you eventually found the answer to your question. I shall give my answer below.
The output y(t) of a system has two components: the free component y_L(t) generated by the initial conditions and the forced component y_F(t) generated by the input signal.
The forced component is the convolution between the causal impulse response h_C(t) (the inverse Laplace of the transfer function H(s)) and the input signal u(t) and has two sub-components: the transitory component y_T(t) related to the system’s structure (influenced by the signs of the poles) and the permanent component y_P(t) related to the input signal (influenced by the input’s poles).
If the linear system is exponential stable, then the free- and transitory components of the output response vanish as the time increase sufficiently, i.e. y_L(t) -> 0 and y_T(t) -> 0 as t-> infinity. Thus, the only component which remains is y_P(t) and moreover, for exponentially stabile systems the permanent component is of the same shape as the input signal as t-> infinity.
BIBO-stability reflects the input-output stability and it is evaluated on the transfer function, H(s). On the state space model one evaluates Lyapunov, asymptotic, exponential and other kind of stability properties.
Consequently:
- If the linear system is internally Lyapunov exponential stable, then for bounded inputs the output responses are bounded, i.e. THE SYSTEM IS BIBO-STABLE;
- If the linear system is internally unstable, but it is also non-minimal such that all the uncontrollable or the unobservable eigenvalues are those with positive sign (within the open right complex half -plane, inducing instability), then THE SYSTEM IS BIBO-STABLE. Explanation: taking into account that the transfer function obtained from the state-space model is always the irreducible, the unstable roots of the characteristic polynomial (poles of H(s)) will be simplified by the similar zeros of the nominator of H(s); consequently, H(s) will have only negative poles which means that the transitory component vanish as time tends to infinity and for bounded inputs the permanent component of the output response will be also bounded as determined by the poles of the input (the Laplace transform of u(t)).
- Conversely, if the transfer function has all its poles with negative real part, i.e. the system is BIBO stable, we cannot know if it is also Lyapunov exponentially stable (the characteristic polynomial can have uncontrollable or unobservable eigenvalues with positive real parts). From a stable transfer function one obtains a minimal state realization which is thus exponentially stable, but this will not reflect the internal state of the system which can be evaluated only on the system mathematical model of differential equations – i.e. the equations which result directly from the mathematical modeling process.
- A transfer function with all its poles in the open left complex half-plane has the impulse response absolutely integrable, i.e. it is L1-stable and vice-versa.
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I would like to store biological samples containing biotinylated proteins at -80 °C for several weeks, before continuing protein extraction and streptavidin affinity purification. I was wondering whether the biotin-protein bond is stable for long periods at -80 °C? Thank you for your advice.
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The biotinylation is unlikely to be a problem, if your protein itself is stable under your conditions. Most proteins are, some are not (especially in complex mixtures where proteases may be present).
As Kiran Shivaiah pointed out, freeze-thaw cycles can be a problem. Apart from his solution to freeze the sample in aliquots you may also consider storage at -20 °C in a glycerol-containing solution. At this temperature, solutions between 50 and 75% glycerol remain liquid, the eutectic is 66.7% with a freezing point of -46.5 °C. I have used this method to store labelled secondary antibodies and found it reliable and convenient.
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If an operating region is divided into a number of sectors and if it is shown that the system is stable in equilibrium point corresponding to each of the sectors, can it be said that the system is asymptotically stable in the entire operating region consisting of each of these sectors? Is there any theorem that can be cited to reinforce the premise?
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Biswajit Debnath Please send me your problem I will try to check the complete stability and get back to you. I got through the concepts from measure theory book and relate to mathematical control on my own. I am sorry I don't have any references to send you. It is my understanding only.
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I'm using the Turbiscan Lab Instrument to assess shelf life and stability properties of my dispersions at different temperatures.
However, once analysing my data, I can only export the graphs into a pdf format.
I couldn’t find a method helping me access my raw data.
Are you aware of any tricks on the software to attain my raw data as a table enabling me to compare and analyse them?
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The simplest method is to manually select and copy the scan data to an excel file. Inside the main Turbiscan software window, you can hold the 'ctrl' button, then left click on the time stamp of the scans you want to copy (usually on the right hand side of the screen.)
Then, right click, select 'copy', then paste them into an excel file. The result will be something like in the attached file. The first column is the height, then transmission, then backscattering data.
From there, I recommend using a Jupyter Notebook (with Python and Pandas) for plotting the data.
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I am working on postural stability during static standing position in condition of using mobile phone and without mobile.
I need literature an suggestion for methods.
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Thnak you Dariusz...
and what you thinking on longitudinal monitoring of large group of participates via mobile app and using of data for science?
Dragan
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I'm currently do my research about stability for gait analysis by using Lyapunov Exponent. Can I calculate the Lyapunov exponent based on the ankle angle and ankle moment? Currently I'm still confusing with the the code steps on how to calculate the Lyapunov exponent. Can someone guide me. Thank you so much.
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Yes, you can practically use any kinematic time series as long its long enough (at least 100 cycles per recording). For more info on the process the following paper is very detailed:
  • Bruijn Sjoerd M.
and
  • van Dieën Jaap H.
Control of human gait stability through foot placement15J. R. Soc. Interfacehttp://doi.org/10.1098/rsif.2017.0816
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I have seen unit cell designs that only perform at normal incidence while there are some designs that perform for a wide range of incidence angles. what is the reason or explanation behind this. what makes them angularly stable.
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In a word, resonance.
Phase on the surface may be related to the phase of an incident plane wave via phase-matching principles and the constitutive relations between wave vector components. So then, observing a large range of incident angles is equivalent to observing a large range of wave vector (k) values on the surface.
If the phase incurred across the metasurface element has a strong frequency dependence, the metasurface will tend to only operate over a small range of angles, which correspond to the frequency/frequencies of operation of the surface mode. Alternatively, if the phase across the metasurface has a weak frequency dependence, it will tend to operate over a wide range of incident angles.
We can visualize these modes on a dispersion (k-Beta or w-k) diagram. Modes which have a strong frequency dependence vs angle will exist over a large portion of these diagrams with some k-dependent slope. Resonant modes, however, will exist as pretty much straight lines -- indicating that over all possible k values, the frequency band stays pretty much constant.
See Yang and Rahmat-Samii's book, "Electromagnetic Bandgap Structures in Antenna Engineering" (ISBN: 9780521889919), Chapter 2, for a more detailed description.
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As MRT express the decay rate (average time that biochar can persist from decaying) and this rate decreases with time. Therefore, the incubation period becomes pivotal for the MRT calculation because shorter duration may lead to higher estimated mineralization rate and shorter MRT. So, can we consider other means of getting justifiable stability period?
please suggest a methodology for above.
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Dear Shiv,
you may check following publications to get some ideas on how to proceed:
Enders et al 2012 10.1016/j.biortech.2012.03.022
Spokas 2010 10.4155/cmt.10.32
Kuzyakov et al 2014 10.1016/j.soilbio.2013.12
Wang et al 2016 10.1111/gcbb.12266
Harvey et al 2012 10.1021/es2040398
and more...
BR
Nils
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In a diverse panel of genotypes, why some genotypes have high stability in certain traits (i.e. flowering time and yield) across multiple environments? In other words, why certain genotypes have consistent or similar phynotypic performance across different environments? Why other genotypes have low stability? Thanks for your help in advance!
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Thanks Joel Ivan Cohen for the good answer to Jiang, its true some phenotypic traits are much heritable across genotypes or varieties and are influenced by the environmental interactions. Take an example of corn crop (similar genotype) tested across different zones that do pose different day length, it will mature at different days, and give different yield even when you provide same rates of fertilizers, water and other agronomic operations like seeding days, seeding rates, timely weeding. The cumulative degree growing days (CDGD) influence on growth stages, and so do to timed operations.
Testing the genotype across environments help you to reveal the hidden traits and also to test performance, and you can be able to recommend same genotype to different growing zones.@Cohen Ivan
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What if the pendulum angle set-point of a inverted pendulum (IP) is not zero? Have you ever tried it?
If the result is the same with the zero set-point , Does it mean that the system is controllable but not accessible?
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the base position (with ref value at zero), and the base acceleration
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As attached in the picture, my emulsion contains Tween80 or food emulsifier occasionally. They both show very opposite but large magnitude of zeta potential. Can i consider this as stable emulsion? Or does anybody know how i could improve.
Tried concentration from 4% to 30% oil
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How did you dilute your samples? Hopefully, not in DI water...
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I'm currently looking into the existing methods of estimating the lightship weight. In particular the estmation of outfitting weight is of interest to me, since it is very dependend on the type of vessel. Ultimately I would like to find out if it is possible to parameterize the outfitting weight for different vessel types.
I would very much like to hear your suggestions on literatur etc. or just your opinions.
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Dear İlkay Özer Erselcan,
Thank you for your input. I will check those books out.
Does anyone have any practical information on how estimation and control of wheights (aka wheight management) is handled at a shipyard?
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I want to use NiCo2O4 as a substrate in 0.5 M H2SO4 solution. Just wondering will it be chemically stable in strong acidic solutions? 
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Hey everyone,
I'm reading the "Stability- and performance-robustness tradeoffs: MIMO mixed.." and I need to simulate everything.
I would like to know if there is a space/place where the Matlab code has been shared, so that I can simulate the reported results as I need.
Is the paper code available anywhere?
If anyone could help, I would be immensely grateful!
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You can find a lot of shared simulink simulations and Matlab codes here in Matlab File Exchange.
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Hi all.
I am looking for clarifications on the hexahedral mixed displacement-pressure elements.
1.) What exactly is the Taylor-Hood hexahedral element? Is it hex element with 20 nodes for displacement and 8 nodes for pressure or 27 nodes for displacement and 8 nodes for pressure? (Considering continuous interpolation for pressure.)
2.) Are both 20/8 or 27/8 elements inf-sup stable? If not, which one is inf-sup stable and which is not? Is there any good reference on this topic?
Thanks.
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I would recommend Section 4.5.2.3 of the following book:
@book{reddy2010finite, title={The finite element method in heat transfer and fluid dynamics}, author={Reddy, Junuthula Narasimha and Gartling, David K}, year={2010}, publisher={CRC press}}
Here, it is said that both Q_2 Q_1 elements with 20 or 27 nodes for the velocities (for fluid dynamics) are LBB-stable.
Taylor-Hood elements often refer to [P_k]^d P_{k-1} or [Q_k]^d Q_{k-1} elements, where k is the polynomial order and d is the dimension.
But there are also other element types that are LBB-stable, e.g., [P_1-bubble]^2 P_1. See for example:
@article{suli2013brief, title={A brief excursion into the mathematical theory of mixed finite element methods}, author={S{\"u}li, ENDRE}, journal={Lecture Notes, University of Oxford}, pages={24--29}, year={2013}}
Hope that helps!
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If I have a MIMO system with a number of subsystems with moderate amount of coupling sensitivity and if those individual subsystems are BIBO stable then under what conditions the whole system can be considered to be BIBO stable ? Is there any necessary and sufficient conditions that needs to be satisfied ? An answer from the control theoretic point of view would be most appreciated.
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Biswajit,
In that case you are trying out some very old concepts afresh !
Not very relevant today perhaps (that's just my opinion, of course !), because control concepts themselves are a lot more mature and evolved today !!
Have you checked out total stability concepts, for instance ?
Cheers !
-Sanjay
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We know that the balancing of load and generation cannot be exactly achieved in a power system. This means that the swing equation cannot be in the steady-state conditions. So in such conditions are the frequencies of a small generating unit and a large generating unit equal?
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Yes, while operating large system, as experienced with proper time stamping measurements done, though average frequency for an integrated synchronous system has been found to be more or less same at each bus under 'so-called' steady-state operating condition (as inherently load changes from time-to-time and so the generation to match) due to sub-transient / transient condition (resulting from disturbances, faults, etc.) variations are not uncommon with coherency and inertia playing significant role.
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Dears all
I would like to know what are the relationships among watershed health, watershed sustainability and watershed stability!
Please share your experiences with me.
Thanks
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A healthy watershed, contributes to watershed stability. Different types of internal habitat and structure diversity also help to diversify the system and provide for increased stability .
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PEDOT:PSS is hygroscopic in nature and absorbs moisture from sorrounding environment. One more problem with PEDOT:PSS is it's acidic nature which affects ITO/HTL interface.These problems lead to degradation of perovskite material and hence stability of PSCs reduced. Now question arises, what are the best solutions to enhance the stability of PEDOT:PSS based PSCs?
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Dear Hassan,
Ramadan Kareem!
I think the solution is in using a metal oxide substitute for the PEDOT: PSS organic hole conducting material. It is found that NiOx is one of the suitable metal oxide hole conductors. For more information please follow the link: https://www.materialstoday.com/energy/news/niox-perovskite-solar-cells-promise-stability/
Best wishesd
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The independence property is defined by Shelah. I am looking for other versions or generalization of the definition in which some circumstances are changed.
Main reference (p.316, Def. 4.1):
Shelah, S. "Stability, the f.c.p. and superstability." Ann. Math. Logic 3, 271–362 (1971)
Another reference: (First Def. in introduction)
Gurevich, Yuri, and Peter H. Schmitt. "The theory of ordered abelian groups does not have the independence property." Transactions of the American Mathematical Society 284.1 (1984): 171-182.
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Can you add a reference to the definition you have in mind?
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Generally it is and industry practice to conduct the accelerated shelf life study of foods products at a temperature of 40+/-5 degree Celsius and 70+/-5% RH. Is there any authentic document which we can refer for this?
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Spectral methods are one of the good tools to find the solution of the PDEs,
I have a parabolic PDE like
dP/dt=f(P, dP/dx1, dP/dx2, d^2P/dx1^2,..)
where f could be
f=a(x1,x2)*dP/dx1 +b (x1,x2)* d^P/dx2+c(x1,x2)*P
I formulated a 2D PDE, but the dimensions could be higher than 2.
a formal way in spectral method to solve the PDE is to solve the eigenvalue problem for operator f like:
f(phi_j)=lambda_j * phi_j
where phi_j is eigenfunctions (preferably orthogonal) and lamda_j are corresponding eigenvalues.
this way we can find the solution of parabolic PDE as well as analyze the stability of the solution based on the eigenvalues.
I should note that the boundary condition might be in Dirichlet , Neumman or Robbin form.
is there any general method to solve this eigenvalue problem and find the eigenfunctions and eignevalues of this general operator?
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Unfortunately the things are much more complex. The Lax theorem is valid for linear schemes but if you look to a proof of convergence for the numerical solution of non-linear equations this theorem cannot guarantee convergence.
For a non-linear formulation, Lax and Wendroff theorem states that if a conservative scheme converges it does towards a weak solution. That means we must previously ensure that convergence exists. (see the texbook of Leveque, page 239)
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I need literature how set-up for markers for 3D analysis of upper body stability with Vicon ( 9 cameras stereophotogrammetric system). Suggestion and advice please.
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Hi Dragan, E. Jaspers and E. Butler have both created an upper limb model to be applied in Vicon. The protocol developed by E. Jaspers has an open-source software toolbox (with matlab) which can be found online.
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I am trying to test some algebraic theory using many different Runge-Kutta schemes, with varying order, number of stages, stability, etc. Does anybody have a reference with a coherent list of lots of established RK schemes and their stability functions? I have pieced together a good number from various books and literature, but an encyclopedia of sorts would be very useful.
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Ben
John Butcher developed the stability theory for Runge-Kutta methods and suspect his book(s) have the Butcher tableau's for many orders and cases.
And it does not require Dr. Dodd's pills like certain matrices.
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Hi,
Let us say that a plant model of the following form is given:
\dot{q} = A*q + B*u,
y = C*q.
The output of the model (y) is its position (x) and velocity (v).
Using this output, I am going to construct a PI controller (u) of the following form:
u = K1*x + K2*v.
Then, the task is to find the optimal gains (K1) and (K2) such that some given cost function is minimized.
Without any constraints, this problem can be solved easily using the MATLAB command 'fminsearch' or 'fminunc.'
But I'd like to add a stability constraint such that the closed-loop system with PI control is always stable.
Mathematically, it is realized by constraining the eigenvalues of the closed-loop system in the left-hand plane.
But I'm wondering how to add this constraint using MATLAB commands.
I tried to use the command 'eig' in the constraint function (nonlcon) of 'fmincon' but MATLAB says that command is not allowed to be used in the fmincon constraint function.
Any comments will be greatly appreciated.
Thank you.
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If the system is second order and the cost function is quadratic then It is also possible to solve suitable linear quadratic (LQ) problem.
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The bifurcation curve generated in MatCont is displayed in the same color(blue). The stability of the equilibrium or limit cycle can only be tracked in the layout of "numeric" in "Window" by Eigenvalues or Multipliers. Does anyone know how to display the stability of the curve graphically by color or any other ways(e.g. line style)?
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We are going to release a new version that supports this functionality, expect something like March 2019.
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I am trying to use Model Reference Adaptive Control (MRAC) based on Lyapunov's rule on a system. My question is: should the reference model be assumed or is there a systematic procedure for determining its parameters in relation to the dynamism of the system in question.
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Dear Demilade . . .
Adapting/adjusting the controller parameters for such cases (where plant parameters were not accurately known) is called adaptive control. so as it can be infer, you should have an acceptable approximation of your dynamic system to tune the adaptive control parameters.
recently i have read a paper about this subject which i want to suggest it to you to read it. its about how to design the law for your MRAC.
it might be helpful.
best regards
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In a simplest case imagine we have a continuous finite-dimensional dynamic system described by and ODE
x_dot=f(x) (1) ,
Is it possible to prove the asymptotic stability of (1) by investigating the discrete time version of (1)
x(k+1)=F(x(k)) (2)
((2) might be written by RK4 discretization, Euler first order descretization or any other descretization scheme)
if it is possible to do that, what about infinite dimensional system resulting from space descritization of PDEs?
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Dear Ali,
your question is interesting. In general, the discrete version will depend on two fundamental choices: the discretization scheme used (there are several) and the discretization time. Notice that it is typicaly not sufficient just to replace t for k and \dot{x(t)} with x(k+1). The stability of discretized models will usually depend on the discretization time. This feature is obviously beyond the continuous-time counterpart.
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in most cases for continuous time stochastic systems which are modeled by SDE, the Lyapunov stability conditions can guarantee the stochastic stability of the system,
another definition In stochastic literature is detailed balance which guarantee the convergence of the probability of the states of SDE to a stationary probability density.
I want to know which one is more strong stability condition?
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With Markov chains having a detailed balance distribution is a stronger condition then having a stationary distribution (that you can check by Lyapunov theory).
Every detailed balance distribution is stationary, but not all stationary distributions are detailed balanced. The proof is very easy. Detail balance means there exist a distribution pi(k) such that
pi(k)q_kj =pi(j)q_jk,
where q_jk is any non-diagonal entry of the generator matrix Q.
Now if on both sides you take the sum over all the k that are different from j you get that stationarity follows (pi Q=0).
You can check it on Durret's book Essentials of stochastic processes, page 130
I'm not sure what happens with diffusions, but it shuold be the same.
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In the theory of the stability of the differential operators, one could prove the stability results based on spectra of an operator, (all eigenvalues must be negative for example).
one problem with the above method is that not all linear operators are self-adjoint (for examples operators in convection diffusion form) and their corresponding eigenvalue problem can not be solved analytically, hence spectra of the operator can not be calculated analytically. On the other hand there is a definition related to spectra, which is called pseudo-spectra, that somehow evaluates the approximated spectrum , even for non self-adjoint operators.
I want to know is it possible to establish stability results for a differential operator based on pseudo-spectra?
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The question you ask is a very broad one. Since differential operators are unbounded - the definition of the on which one defines the operator is important. When one goes to infinite dimensions, there might not even be a point spectrum (eigenvalues) - the spectrum may be only the continuous spectrum and residual spectrum. If the operator has a self joint extension or a normal extension then the problem becomes more tractable but for non-normal operators the problem is quite complex.
At one time a class of operators "spectral operators" were defined, see Dunford and Schwartz, "Linear Operators", vol III, to address the issues on non-normal operators. Proving a non-normal operator - even an ordinary differential operator - was not a trivial task. The goal of this effort was to expand the concept of Jordan Canonical form to first bounded linear operators on a Hilbert/Banach space and then to unbounded linear operators, e.g., differential operators. For compact operators or operators with compact resolvents - that has been solved. For bounded normal and unitary operators, that has been solved (spectral theorem). For unbounded operators with a compact resolvent, that has been pretty much solved (by using the spectral theorem the spectral theorem). For unbounded self adjoint operators, there is also a spectral theorem. However, for non-normal bounded operators and non-self adjoint unbounded operators - there is no general result on a canonical form.
In these problems stability questions be quite problem specific.
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Is there any scientific data avaibale on the AAV vector stability in 15-20% Tween 20 solution? Also any information on the AAV9 aggregation behaviour at 6E+13 concentration range? 
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Hi Navneet,an AAV at the titer of 6E+13 would not aggregate, we can produce as high as 1E+15, no aggregation was observed.
You could find more on the website: www.genemedi.net/i/aav-packaging
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Could there be nonlinear ODEs that could not even be solved numerically?
I am working on a third-order nonlinear problem which is giving accurate results for a given set of initial conditions (ICs) but for other ICs the matlab ODE solver (checked 4-5 algorithms) do not converge.
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If your equation/system of equations is prone to stiffness or strongly nonlinear the ode 45 solver may not be adapted for some ICs because it uses a fully explicit numerical scheme. This page can help you to chose better adapted solvers: https://www.mathworks.com/help/matlab/math/choose-an-ode-solver.html
If none of these solvers works then you may need to write yourself a numerical scheme adapted to your case, probably an implicit or semi-implicit scheme (more stable than explicit schemes) since matlab solvers don't work.
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Hi,
I was wondering if anyone has experience with the stability of lyophilised human hemoglobin after being dissolved in solution (e.g., MilliQ water, tap water or buffer) and stored at 4oC, -20oC or -81oC for weeks/months?
Thank you.
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Greating!
You can read the following links that may be useful to answer
..........
With best wishes
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I am trying to study the stability of lattice Boltzmann method. The the eigenvalues of the evolution matrix in wave number space need to be studied carefully.
I solved the eigenvalues using Matlab.
I thought that the fluctuation is an artifact resulting from using Matlab, since it shifts the order of the eigenvalues each time I am calculating them. However, this is not the case.
To prove that, I derived the characteristic polynomial and found analytical solutions for each mode. The analytical solution is correct, however some modes fluctuate between it self and other mode (see the picture). Note: there is another mode that complement this mode, so that they together form complete two modes.
what is the reason for this fluctuation? and what is its impact on stability and accuracy?
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Thanks Ahmad. That answered part of the question. I will try to explain what I understood. The eigenvalues are fluctuating because eigenvector can be recombined through linear combinations. So, there is a specific set of eigenvectors that generate non- fluctuation eigenvalues. Please correct me If am wrong.
I want to know also if this fluctuation has any impact on stability or accuracy of the analyzed method?
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Here, by element-wise bound, I mean bounds on each of the elements of A, B, and P matrices.
i.e., |aij| <= a0ij >=0, etc...
Also, P is the solution to the Algebraic Riccati Equation.
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Thank you for your replies. BTW, I think I have also found a direction which can lead to some insights about this problem.
A matrix defined by having element-wise bounds is known as an interval matrix.
A linear system whose system matrices A and B have element-wise bounded uncertainty, are known as linear interval systems. We need to find the interval matrix corresponding to the riccati solution P. Keywords: interval matrix, linear interval system.
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for deterministic systems, with defining proper terminal constraint , terminal cost and local controller we can prove the recursive feasibility and stability of nonlinear system under model predictive control. For stochastic nonlinear system it is impossible to do that since we do not have bounded sets for states.
what is the framework for establishing the recursive feasibility and stability of MPC for stochastic nonlinear systems?
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bounded uncertainty is a robust approach not stochastic approach.
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Please describe your opinion on this topic and suggest some literature.
Effects and mechanism of control during chewing gum in quite standing position.
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Mastication of chewing gum improved the postural stability during upright standing in some studies. Explanation may lay in activation of mastication muscles, condition of temporomandibular joint and trigeminal proprioception. I suggest this study to confirm the opinion:
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We are working on some projects related to networks of coupled nonlinear oscillators. We want to obtain “Master Stability Function” (MSF) in our network.
1. Is there any sample code available in the internet for it (we searched, but we couldn’t find any)?
2. Can someone please introduce us some papers who have obtained MSF for simple examples?
3. Is there any major difference between 2D systems and 3D systems in the procedure of calculating MSF?
Let me say everything in an easier way. Suppose that we have only 2 identical Lorenz systems, which are coupled through variable “x” with the coupling strength “d”. How can I obtain MSF when I change “d”? Is there any available code for it? If you have any answer for this question, is it applicable and meaningful for two identical Van der Pol systems (which are 2D) which are coupled through variable “x” with the coupling strength “d”?
Many thanks in advance,
Sajad
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Hi
I think this paper that could help you
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I would like to know which assays can be performed to study the stability of antibodies.
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Hi Rita -
The stability of antibodies is an essential part of any antibody development program. One essential method is size exclusion chromatography (SEC-HPLC), which allows you to monitor aggregation.
There are many different conditions on how to run SEC, but my favorite by far is the SMAC method mentioned by the team at Merrimack using our Zenix column.
The article unfortunately isn't published on research gate, but if you can get your hands on a copy, it really is a great read!
If you're in need of a starting place for running conditions, this link might be useful as well: https://www.sepax-tech.com/samples_app.php?sample=Antibody
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Is it possible to generalize chemical stability of group of materials versus the others? For instance, can we arrange oxides, fluorides and haloids in an order from most to least chemically stable ?
The term "Chemically stable" sounds confusing too. When we say a material is chemically stable, are we including factors such as Temperature, Pressure, pH of medium, etc all at the same time ? I'm asking this question because I saw in a reference that they said Oxides are more chemically stable than Fluorides. While, in another paper the exact opposite claim was mentioned without any condition explanation.
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Hydrogen floride etches oxides such as silico dioxide and aluminum oxide. So, most oxides are not stable against HF.
Best wishes.
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Is there anybody with an insightful note or explanation on how to establish the stability of the solution of ODE (bvp) using Poincare-Lyapunov Theorem?
Reduction of the bvp to initial values problem and generation of the Lyapunov function do not incorporate the boundary conditions. We believe these are not acceptable.
Do you know how to include the Neumann boundary condition into Jacobian matrix or how to generate Lyapunov function suitable to establish the stability of the solution of ODE bvp; see the attached problem.
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The notion of stability for BVP is different than the notion of stability for IVP. Hence the standard linearisation theorem cannot be directly applied.
The main question that you want to address is: what does it mean for a solution of a BVP to be stable (with respect to what perturbations). So, you need a definition.
If the problem comes from a variational formulation based on the energy, then looking at the positive definiteness of the second variation is the standard way to define and prove stability. Intuitively, the question is to see if nearby solutions around a given solution have lower energy. You can see examples in my paper with Thomas Lessinnes that deals with Neuman conditions. In particular we give a full computation for a simple 2nd order system for which we establish stability. Maybe it would be helpful if this is what you have in mind. Otherwise, you will find references in there.
The reference is
T. Lessinnes and A. Goriely, 2017 Geometric conditions for the positive definiteness of the second variation in one-dimensional problems. Nonlinearity 30, 2023..
And I believe that it can be found on research gate (or ask for it).
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I am using the DSATools software to do a simulation of four generators eleven buses. Firstly, I suppose to do a simple simulation with single machine single line. However, I don't know how to use the PSAT and how to calculate the parameters of the load.
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Dear Shiqi Cao,
I suggest you to see links and attached files in topic.
- An Open Source Power System Analysis Toolbox - CiteSeerX
- PSAT Model- Based Voltage Stability Analysis for ... - Semantic Scholar
- Optimal Placement of STATCOM to Voltage Stability Improvement and ...
khartoumspace.uofk.edu/.../Analysis%20of%20Power%20Systems... -A Practical Method for Power Systems Transient Stability and Security
Best regards
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I have to design a fractional order PID controller for a maglev plant. The maglev plant is an open-loop unstable system. Its transfer function has two real poles, one on the RHS of s-plane and one on the LHS of s-plane, G(s)=-K/(s2 - p).The controller parameters are tuned using an evolutionary algorithm.
For a particular set of the controller gains I achieve good closed loop response.I have attached the figure of the system response. However, frequency domain analysis (bode,nyquist and nichols-chart) of the system, using MATLAB, shows negative Gain Margin and positive Phase Margin. I have attached the Nichols Chart obtained from MATLAB.
It shows that the gain margin is negative. But says "Yes" to "Closed loop stable?"
How do I correlate these facts? The system exhibits stable response. But the Gain margin is negative! How so?
Is the system actually closed loop system? If so, then how?
Please clarify. I am perplexed!
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Gain margins is defined by 1/|G(jw)|, where G is your frequency response. So now if |G(jw)| is bigger than 1, you will have a margin in dB which is smaller 0dB.
This does not tell you about the stability of the system.
To validate the stability you have to validate stability criteria like the Nyquist criterion, where you count the encirclement of of the critical point at -1 and compare if to the necessary ones to be stable. (in your case Matlab does it for you :) )
That said, you can have a negative margins and a stable system, like in your case. Do not judge system stability by margins, as they are not defined for unstable systems, but of course, can be calculated if you just take the equation from the first line.
Hope that helps.
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for ODEs we can use the definition of stability,
for example when the ODE is linear, by calculating the
Eigenvalues or poles of the system the stability characteristic of the system can be achieved. or in nonlinear case the Lyapunov theory of stability can be used.
do such definitions (equilibrium point, stability, Lyaponov theory) exist for PDEs?
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Besides the the above mentioned internet sites, it could be of certain interest some chapters of the book by Zauderer “Partial Differential Equations of Applied Mathematics”, Third Edition, Wiley, N.Y. (2006).
In certain cases, the analysis of the solutions of a boundary value problem for a nonlinear PDF can be done introducing coupled modes of evolution that reduces the problem to one of stability analysis of the solutions of an ODF, as suggested in the attachment. This approach appears in the book by Wicktor Eckhaus, “Studies in Nonlinear Stability Theory”, Springer, N.Y. (1965).