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Thread: Van der Waals and Bremsshralung radiation from Sonoluminscence

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    Van der Waals and Bremsshralung radiation from Sonoluminscence

    abstract

    After some derivations, I have reached some theoretical equations that wish to attempt to explain corrective energies to sonolumiscence. By taking into consideration that the bubble wall velocity increases, charge particles inside of the bubble could very well be caught in this motion, collectively giving off an energy satisfying the equations of motion for the logarithmic spiral. We also study a form of the equation which takes into account any Van der Waals forces between the particles, before being dominated by the large thermal contribution.


    My original derivations looked a bit messy so I sought a simplification. The ordinary equation was







    Distribution of the density and simplifying some terms I get





    Integrating the volume element we obtain the simplified version of our equations



    or







    With being a charge density and The dimensions of this equation is force over length or energy over area. It has an ‘’acoustic energy’’ part given by and a wall velocity term . This part can be seen in terms of an ''acoustic intensity'' term. It’s also been known for the surface tension to have a coefficient of where is the critical temperature (known as the Guggenheim–Katayama formula). As temperature increases the surface tension decreases.

    [1] - an alternate simplification from a previous Langrangian of the theory we formalised, requires only the additional binding or repulsive energies from Van der Waals forces





    (which is the Langrangian)

    The repulsive nature could temporally explain the expanding of the bubble but it seems more likely related to pressures and temperature.

    [2] - Further, there is a part of this equation



    Namely this expression can be fashioned in a different way:



    This is not too far from the difference of such a potential which actually gives rise to the Lamb shift, a direct consequence itself of the vacuum energy, ie. Casimir effect, par the powers of the fine structure



    This was all possible from theoretical assumptions being added to the physics of the Rayleigh-Plesset equation which took into account thermal variations - which now, we give in the form with additional assumptions made about the wall kinematic viscosity with the motion of charges inside of the bubble:





    The equations for the expanding and collapsing bubble was very similar to those of the Friedmann equation and it gave me some possible insights into the suggested ''corrective terms.''
    Last edited by Dubbelosix; 2018-Jun-01 at 01:27 PM.

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    Dear Dubbelosix
    You might want to consider to give a bit more information here, because (for me and I suppose others) the "introduction" leaves me bewildered about what is going to be presented and then you jump into a set of equations of which I (and probably others) have no idea what they are supposed to describe and why the = signs that you give are valid.
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    Quote Originally Posted by tusenfem View Post

    Dear Dubbelosix
    You might want to consider to give a bit more information here, because (for me and I suppose others) the "introduction" leaves me bewildered about what is going to be presented and then you jump into a set of equations of which I (and probably others) have no idea what they are supposed to describe and why the = signs that you give are valid.
    Sure. I'll take people through the entire derivation.... Will take some time, but at least people won't be so clueless.

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    the Reyleigh-Plesset Equation and the Friedmann equation share some common features yet I also explained, this was due to the fact they both describe similar physics founding the fluid expansion and collapse modes of the Friedmann equation for a spherical homogeneous distribution of matter.
    Let’s draw in on those relationships first, then we will be able to proceed further with my ideas.

    The Rayleigh-Plesset equation is



    In which the following variables are defined as:

    ρ - is the density (https://en.wikipedia.org/wiki/Density) of the surrounding liquid, assumed to be constant
    R(t) - is the radius of the bubble which when taken as a ratio with itself is by definition related to the scale factor which also features implicit time dependence.
    ν - is the kinematic viscosity (https://en.wikipedia.org/wiki/Kinematic_viscosity) of the surrounding liquid, assumed to be constant
    γ - is the surface tension (https://en.wikipedia.org/wiki/Surface_tension) of the bubble-liquid interface

    I have noticed, from my own work, that the fluid expansion plays a role of coefficient on all the terms in the non-conserved definition of the equations. Nevertheless, the definition above too also implements a fluid expansion of its own. Of course, expanding universes and expanding ‘’bubbles’’ require the same base mathematics. Let’s take a look at one formulation of the equations I have written in the past. If we take one of the time derivatives (preferrably the second term) as a curvature term then we can modify the dynamics of the Reyleigh-Plesset equation in some unique ways. We can also add density and pressure terms, which, if you take relativity seriously enough like I do, then it should be in there. First let us look at a few equations I derived, and then after let’s assume an object can be created from it. The equations which feature similar terms are:







    The last term refers to rotating systems and so will produce Larmor radiation, or known as the Cyclotron radiation. **Since the viscosity actually refers to the motion of the fluid around the bubble then any charged particles compressed to the region [will] exhibit the behaviour of this equation above!** Comparing these results with the Reyleigh-Plesset equation



    (since surface tension is then we may derive from the last equation a direct proportionality with viscosity )
    (which is another form to write it with terms appearing on the right hand side of the equation) and courtesy of wiki, I extract a quick set of definitions for the terms:
    ‘’This is an approximate equation that is derived from the Navier–Stokes equations (https://en.wikipedia.org/wiki/Navier...okes_equations) (written in spherical coordinate system (https://en.wikipedia.org/wiki/Spheri...rdinate_system)) and describes the motion of the radius of the bubble *R* as a function of time *t*. Here, *μ* is the viscosity (https://en.wikipedia.org/wiki/Viscosity), *p* the pressure (https://en.wikipedia.org/wiki/Pressure), and *γ* the surface tension (https://en.wikipedia.org/wiki/Surface_tension). ‘’

    It becomes a lot clearer why the dynamics are similar, at least, in respect of like terms. We may use the previous equation later, but I want to concentrate just for now on this form of the equation



    Simply because (it formats) the terms very clearly with relationships to each other and also, it is this form of equation (when setting it to zero) can you formulate a Langrangian. Let’s have a look at that (what I will call this time) the Reyleigh-Plesset Langrangian:

    All we do is assume distribution of a mass term



    There are some obvious crucial dynamical differences between this equation and the Friedmann equation only within heuristic framework. In fact, drawing on sonoluminiscence, we may think a compression of the material exerted by the forces imploding the material inside the bubble to be nothing more than a cold fusion which releases a large amount of energy. There was detection of excess neutrons from no external source supporting this notion that some kind of fusion is occuring. There is also tantalizing situations and arguments for the case of it being vacuum related, since the amount of energy released can perhaps provide more energy than what can be taken from thermonuclear reactions has been postulated by a number of authors. The kinematic viscosity (https://en.wikipedia.org/wiki/Kinematic_viscosity) of the surrounding liquid is often assumed constant but **it is very likely** phase transitions do occur when the bubble expands and inexorably implodes.
    Last edited by Dubbelosix; 2018-Jun-01 at 01:37 PM.

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    Let’s jump straight into it. From the last post the two equations which interested me was:





    With the last equation I stated:

    The reason why this was stated because it is believed by a number of scientists that Larmor radiation from accelerated charged particles may be a contributor to the phenomenon. Based only on the fact that magnetic fields have been detected around the ‘’star in a jar’’ - I think this is possible since a rotary feature gives rise to a closed current in which charged particles could be bound in a high momentum, giving off Larmor radiation. Certainly the amount of energy from the source, (if it cannot be described alone by nuclear fusion) could have other additional contributors. Another equation which interested me was the proposed Langragian of the theory:



    (The fluid equation using relative consequence of with \ $where is of course the density and features standard notation for the pressure).

    However, from this point on, if those who can use the equations to find that Larmor radiation from accelerated particles within the framework of the ‘’reaction’’ can fully and adequatly explain the energies observed emitted from the source then I would now be inclined not to think of a nuclear reaction explanation but one primarily induced from accelerated particles from the weak equivalence of general relativity. For instance, the viscocity **should **have an effect on the bubbles interior particles if it contributes to angular coupling of momentum to the interior particle motions. It would be similar why, we expect a rotating universe would mean the systems inside of it owe its own property of rotation to the same effect.

    In such cases, magnetic fields do in fact exist, even if the electric forces have tended to zero! Now… there are a few ways to continue from here, but I think I have found the most simplest way to continue: We’ve established from my point of view that if Larmor radiation is involved here then this equation



    Will also then require to add new terms to account for rotational radiation from accelerated motion of charges. According to wiki:

    ‘’This equation, though approximate, has been shown to give good estimates on the motion of the bubble under the acoustically (https://en.wikipedia.org/wiki/Acoustics) driven field except during the final stages of collapse. Both simulation and experimental measurement show that during the critical final stages of collapse, the bubble wall velocity exceeds the speed of sound of the gas inside the bubble.’’

    Then already we have an immediate connection between the viscocity of the surrounding fluid and possible increasing temperatures from the accelerated charges contained inside the bubble, under tremendous pressure and possibly strong density (compared to elements on the periodic table). Regardless, it should be obvious this important because the Reyleigh-Plesset equation is only approximate towards its final stages, in which the bubble undergoes it’s imploding feature - If it had explained this phase transition, today the phenomenon would not have been such a phenomenon.
    Last edited by Dubbelosix; 2018-Jun-01 at 01:37 PM.

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    Spiral trajectories for charged particles will follow on to the jerk and then higher derivatives such as



    and is a continuous function unless electrons collapse towards the center - since we do not know the full dynamics and that some have suspected some nuclear fusion of sorts to be going on during the high temperature phase, anything is possible. If they where to collapse and add energy to fusion, then Larmor radiation definitely is involved. The above has dimensions of power so it can be written as such:



    Ignoring this definition though, the path we take will be to find an analogous Friedmann ‘’set-up’’ for the Reyleigh-Plesset equation of the form (ignoring additional constants):



    featuring the charge to mass ratio coefficient. Either way, this is stil not the equation we will investigate, we need to simplify a bit more:



    This term describes the fluctuations of a vacuum energy contribution as



    or in the form we suggest



    Which allows the dual production of photon pairs from the vacuum energy directly. It’s also curvature dependent because in this particular theory, curvature is a mechanism for giving virtual particles into real boosts. It's also unlikely I will take into too much serious consideration a vacuum energy explanation.
    Last edited by Dubbelosix; 2018-Jun-01 at 10:37 PM.

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    Now...

    ms of the Rayleigh-Plesset equation. Not only is this adding to the difficulty of me going forward, there is in hindsight loads of different variations of the Rayleigh-Plesset equation for different perspectives and different kinds of physics. Of course our ultimate goal is to solve one issue it has concerning a temperature gradient. The very structure of the equation is inexorably more complicated than the Friedmann equation it seems, because there are not only boundary conditions but with it extra variables making it a complicated equation overall. The more variables you have, the harder it is to solve an equation like this. For instance, we have new variables like which is the material derivative, which is the sum of all steady and unsteady pressures outside of the bubble. the pressure at the boundary within the fluid. the sum of all steady and unsteady pressures in the gas. the sum of all steady and unsteady pressures in the bubble interior. as a vapor pressure. pressure in the liquid at the bubble wall. is the static pressure in the liquid outside the bubble wall. Then in limits, is the assumed magnitude of far from the bubble. Small will be reserved for the range from bubble center and large for the bubble radius itself. in common notation is the liquid particle velocity... and so much more which makes this one of the harder equations we will have investigated. - it seems like we should cover why the Rayleigh-Plesset equation is what it is, work with a simple framework to start it off. To do this we will need to derive the equation along the thought-processes which led Reyleigh and Plesset to their discovery.

    **Derivation of the Reyleigh-Plesset Equation in terms of Energy Balance**

    A spherical gas ''bubble'' in an incompressible liquid has a fluid velocity which falls off as an inverse square law with range $r$ as a result of the liquid incompressibility (which is an assumption of the theory).

    The velocity is



    Where here, is once again the bubble radius with this time, interpreted as the wall velocity. The bubble can change, in a Friedmann equation, this is also true as it pertains to an expanding or collapsing metric.

    As the bubble radius changed, from an equilibrium at to some other, work is done on the bubble by that pressure which would exist at the location of the center of the bubble. There is experimental evidence that all the dynamics are in fact resulting from a varying pressure inside the bubble giving rise to the new physics found in sonoluminscence.

    If the spatial scales over which the pressure changes are much greater than the bubble radius than this almost equals the liquid pressure far from the radius .

    It is said here, that is an included dynamic component, but really the object looks very similar to that found in the effective density of a Friedmann equation which features as - they arise as a relativistic consequence. In previous work, when another derivative of time featured giving the non-conserved solutions of a Friedmann equation, a temperature gradient could have been added directly from a fluid/state equation.

    The difference between this work and the work done by the pressure at the bubble wall will equal the kinetic energy in the liquid:



    The balance equation states that



    Differentiation of this with respect to gives



    The terms on the left arises from the difference in the work done at the bubble wall and remote from the bubble and the terms on the right arise from the kinetic energy imparted to the liquid. Note also from this last object we can form:



    If the pressure far from the bubble comprises both a static component $p_0$ and an applied driving pressure $P$ then this can be expressed giving the Rayleigh-Plesset equation of motion



    ignoring additional constants. And we did what we wanted for this post, which was deriving the Rayleigh-Plesset equation, but really, we derived it also for the second last equation because its likely we will come back to the second last equation with physics learned from Friedmann cosmology.


    **References:**
    http://brennen.caltech.edu/fluidbook...etequation.pdf (http://brennen.caltech.edu/fluidbook...etequation.pdf)
    https://eprints.soton.ac.uk/45698/1/Pub9182.pdf (https://eprints.soton.ac.uk/45698/1/Pub9182.pdf)
    simpler version which we will look at have been seen in literature: https://www.researchgate.net/post/Ho...esset_equation (https://www.researchgate.net/post/Ho...esset_equation)

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    The wall velocity has to be proportional to a dragging or inertial effect on the surrounded gas bubble coupling to inerior dynamics, similar again, to Friedmann cosmology in the rotating model, when early galaxies tended to align themselves with the rotatonal motion of the horizon of a universe. A good thought analogy, though different physics, is how electrons align themselves in a Stern-Gerlach experiment when electrons tend to align themselves towards the magnetic lines of force. An early rotating universe is also expected to have primordial magnetic forces.

    The wall velocities are intrinsically part of the functions giving rise to the LHS of the equation. Those velocities also satifsied Larmor radiation from the spiral trajectories or accelerated motions which I have already given as a relationship satifying:





    Where we define as a ‘’central potential’’ related to rotating systems. Note also the potential depends on the bubble radius.

    It may become an important additional to any equation we submit in this work as ‘’a candidate’’ to explain dynamics outside of the normal Reyleigh-Plesset equation. I have no idea whether the gradient of the temperature has been considered from the simplified form of the Reyleigh-Plesset equation of the form:



    We have a temperature gradient allows a logical modification of the Reyleigh-Plesset equation - best bit is, we didn’t use any ad hoc statements to get there since within general relativity, the relationship ratio’s hold in hydrodynamics combined. The equation of state in my original cosmology studies which allowed a Friedmann equation to explain anistropies took the form:



    As I said before, the equation confirms the existence of an effective density component based on the assumptions made about $p_{\infty}$, since, if the spatial scales over which the pressure changes are much greater than the bubble radius than this almost equals the liquid pressure far from the radius $\rho_{\infty} = p_0 + P(t)$. This result can be seen in complete analogy with the effective density found within Friedmann dynamics $\rho + P$ which makes me wonder if we can extract that physics and redefine the Reyleigh-Plesset equation in a way, but hopefully a dynamically interesting one. The obvious way forward, is that if $p_{\infty}$ arises dynamically synonmous with the reasons the effective density arises in the Friedmann equation, then maybe the two could very well be replaced with each other - it doesn’t seem to harm the physics in my mind, so long as we do not forget the real reason why the equation’s internal dynamics are actually rotating —- simply due to the viscosity of the surrounding incompressible fluid.

    In order to do that, we will need to take another look at some key equations that will provide insight how to move forward, those are:







    An obvious relationship first we can construct relies in the kinematic energy density of the system which is proportional to the proper density



    Also from the equation with richer dynamics, we can construct the energy of the system as



    (this is just all notes we are making right now). It’s not leading anywhere specific. The Reyleigh-Plesset equation was:



    In the Friedmann equation I have shown, actually features like terms:

    Last edited by Dubbelosix; 2018-Jun-01 at 01:29 PM.

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    And finally this sums it up. I Suggested in the previous that the equation takes the form



    with . In terms of its latent heat, a certain approach taken in literature, is that as the bubble shrinks and passes through its equilibrium radius, the condensate will be destroyed and discharge its energy. This kind of model predicts that the each condensate stores an amount of latent heat energy released in the discharge given by the following:



    - constant volume heat capacity per mole of the gas in the bubble
    -is the ideal gas constant
    - is the ambient atmospheric pressure
    - the number of moles of gas in the bubble
    - the Van der Waals excluded volume per mole (notation may vary)

    One mole of gas under the ideal gas law is:



    Next assume that all particles are hard spheres of the same finite radius r (the van der Waals radius), the effect of the finite volume of the particles is to decrease the available void space in which the particles are free to move - something we briefly covered in previous parts - the momentum is subject to the commutation property with position of the particles. We must replace the corrected equation becomes using the excluded volume is



    $b'$ is well-known to be four times the proper volume of the particle. The excluded volume is an important feature in the Van der Waals formula ~



    where is the temperature and is a pressure. The Van der Waals formula consists further another additional feature which describes the attractive properties of the particles at certain distances,



    feature the molar mass volume $V_m$. In which $a$ a measure of the average attraction between the particles - it has the form of and . It also features is Avagadro’s constant with a Boltzmann constant coefficient . The Loschmidt constant

    (https://en.wikipedia.org/wiki/Loschmidt_constant) is



    If we take a dynamic pressure inside of the bubble then the modified Rayleigh-Plesset equation can take into account the additional interparticle forces









    where is the number density. As you can see, no need to introduce any new additional features on the RHS when taking into consideration Van der Waal forces. Alternatively the pressure can be entirely understood as



    In which case another form of the equation to be studied will be







    **References:**
    Avogadro constant - Wikipedia (https://en.wikipedia.org/wiki/Avogadro_constant)
    Van der Waals equation - Wikipedia (https://en.wikipedia.org/wiki/Van_der_Waals_equation)
    Last edited by Dubbelosix; 2018-Jun-01 at 06:50 PM.

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    Quote Originally Posted by Dubbelosix View Post
    abstract

    After some derivations, I have reached some theoretical equations that wish to attempt to explain corrective energies to sonolumiscence. By taking into consideration that the bubble wall velocity increases, charge particles inside of the bubble could very well be caught in this motion, collectively giving off an energy satisfying the equations of motion for the logarithmic spiral.
    Which logarithmic spiral? Is this an ATM (Against The Mainstream) theory?
    We also study a form of the equation which takes into account any Van der Waals forces between the particles, before being dominated by the large thermal contribution.


    My original derivations looked a bit messy so I sought a simplification. The ordinary equation was







    Distribution of the density and simplifying some terms I get

    It appears that you have multiplied both sides of the equation by , except the subscript "waals" has been removed for some reason.


    Integrating the volume element we obtain the simplified version of our equations

    Integrating the right hand side with respect to V, does result in the "constant" terms just being multiplied by V, but that is *not* the case for the terms that have 1/V or 1/V2 factors.

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    Quote Originally Posted by grapes View Post
    Which logarithmic spiral? Is this an ATM (Against The Mainstream) theory?

    It appears that you have multiplied both sides of the equation by , except the subscript "waals" has been removed for some reason.

    Integrating the right hand side with respect to V, does result in the "constant" terms just being multiplied by V, but that is *not* the case for the terms that have 1/V or 1/V2 factors.
    Yes, the subscript I think here, I just replaced for a bolded version to differentiate the difference.

    ''Integrating the right hand side with respect to V, does result in the "constant" terms just being multiplied by V, but that is *not* the case for the terms that have 1/V or 1/V2 factors.''

    My calculus is a bit rusty, can you explain why? The way I deduced this, was through a dimensional analysis, the appearance of a volume element on the LHS would reduce the dimensions of all other terms on the RHS.

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    Quote Originally Posted by grapes View Post
    Which logarithmic spiral? Is this an ATM (Against The Mainstream) theory?
    I used a logarithmic spiral equation which calculates the power given off by charged particles on those types of trajectories. I don't know if it is against the mainstream, the problem is there is no consensus on anything here.

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    Oh right yes, you can also write it as the log Grapes, if this is what you meant. It actually never occurred to me to write it like that.

    Like this?

    integrating volume element gives:


    using:






    Last edited by Dubbelosix; 2018-Jun-01 at 06:15 PM.

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    Quote Originally Posted by Dubbelosix View Post
    ''Integrating the right hand side with respect to V, does result in the "constant" terms just being multiplied by V, but that is *not* the case for the terms that have 1/V or 1/V2 factors.''

    My calculus is a bit rusty, can you explain why? The way I deduced this, was through a dimensional analysis, the appearance of a volume element on the LHS would reduce the dimensions of all other terms on the RHS.
    Rusty?

    Well, that's not the way integration works at all!

    Quote Originally Posted by Dubbelosix View Post
    Oh right yes, you can also write it as the log Grapes, if this is what you meant. It actually never occurred to me to write it like that.

    Like this?

    integrating volume element gives:


    using:
    That's headed in the right direction, but that equation is wrong, obviously. You may be missing a few symbols? Did you forget some?




    No, that's definitely wrong!

    Hey, this is the first few lines of your first post. You might want to oil up your calculus, if it is that rusty.

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    Quote Originally Posted by grapes View Post
    Rusty?

    Well, that's not the way integration works at all!


    That's headed in the right direction, but that equation is wrong, obviously. You may be missing a few symbols? Did you forget some?

    No, that's definitely wrong!

    Hey, this is the first few lines of your first post. You might want to oil up your calculus, if it is that rusty.
    Heading in the right direction?

    Maybe you could be a gentlement and refresh that memory? You said I was heading in the right direction, so since I am almost there, why not be a bit more clear. It's not like you are harboring secrets.

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    Quote Originally Posted by grapes View Post

    That's headed in the right direction, but that equation is wrong, obviously. You may be missing a few symbols? Did you forget some?
    Did I forget something, let's see? Yes I did,



    Last edited by Dubbelosix; 2018-Jun-02 at 04:26 PM.

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    Quote Originally Posted by Dubbelosix View Post
    Did I forget something, let's see? Yes I did,



    Do you have an actual ATM idea that you are prepared to defend here? So far it seems that you are merely presenting a series of badly executed homework exercises. While no doubt thrilling to you, watching someone else work out first-year maths holds rather less interest for others.

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    Quote Originally Posted by Geo Kaplan View Post
    Do you have an actual ATM idea that you are prepared to defend here? So far it seems that you are merely presenting a series of badly executed homework exercises. While no doubt thrilling to you, watching someone else work out first-year maths holds rather less interest for others.
    That's very condescending of you isn't it?

    Personally, just looking at some of the standards of the threads posted in this subforum, I would have thought this would be a refreshing change.

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    The idea I am defending here are corrections to the Reyleigh Plesset equation. It's an entirely new way to view this equation because it takes into respect the cyclotron radiation from rotating charges inside of the bubble cavity.

    If you cannot appreciate a good discussion in physics, maybe you should not try.

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    Also I would like to defend, there is nothing ''simple'' in what I have done. Just because it looks like I have used a simple algebra, does not take away the computation a person has to put in to make sure you are tracking dimensions. It takes study and an understanding of what you are doing to do this in the first place. I put intuition from my Friedmann studies to understand how to put in the pressure from Van der Waals forces and found a direct way to plug in equivalent terms for the radiation from cyclotron motion.

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    Quote Originally Posted by Dubbelosix View Post
    The idea I am defending here are corrections to the Reyleigh Plesset equation. It's an entirely new way to view this equation because it takes into respect the cyclotron radiation from rotating charges inside of the bubble cavity.

    If you cannot appreciate a good discussion in physics, maybe you should not try.
    Good discussions in physics are always welcome here at CQ. However, the ATM forum is for a very different and specific purpose. You are labouring under a misapprehension that perhaps stems from not having read the rules of the forum (link is in the mod's signature, for your convenience).

    Again, the fact that you are still attempting to get first-year calculus correct tells us that you are not near ready to defend your idea. Perhaps you would consider working out the details first, rather than expecting a collaborative development here.

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    Quote Originally Posted by Dubbelosix View Post
    Also I would like to defend, there is nothing ''simple'' in what I have done. Just because it looks like I have used a simple algebra, does not take away the computation a person has to put in to make sure you are tracking dimensions. It takes study and an understanding of what you are doing to do this in the first place. I put intuition from my Friedmann studies to understand how to put in the pressure from Van der Waals forces and found a direct way to plug in equivalent terms for the radiation from cyclotron motion.

    Maybe a good way of starting a thread like this is by actually telling the people what you want to discuss, because most likely few will know what the Reyleigh Plesset equation is, let alone why this need the correction that you claim to introduce here. So, I would advise you, as I did in my first comment, to actually tell us what you are going for here.
    Also, it might be good not to post immediately 7 pages of calculus, when you claim yourself you are rusty on the topic. Small steps also get you towards your goal.
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    Quote Originally Posted by tusenfem View Post

    Maybe a good way of starting a thread like this is by actually telling the people what you want to discuss, because most likely few will know what the Reyleigh Plesset equation is, let alone why this need the correction that you claim to introduce here. So, I would advise you, as I did in my first comment, to actually tell us what you are going for here.
    Also, it might be good not to post immediately 7 pages of calculus, when you claim yourself you are rusty on the topic. Small steps also get you towards your goal.

    I have explained what we are doing, I will explain it simpler - the Reyleigh Plesset equation describes the physics of an expanding and collapsing bubble. The equation does not work well though:

    ‘’Some have argued that the Rayleigh–Plesset equation described above is unreliable for predicting bubble temperatures and that actual temperatures in sonoluminescing systems can be far higher than 20,000 kelvins. Some research claims to have measured temperatures as high as 100,000 kelvins, and speculates temperatures could reach into the millions of kelvins. Temperatures this high could cause thermonuclear fusion.’’

    So we have a temperature gradient which is one unique change in our approach. Since magnetic field have been detected around the phenomenon, it's very likely Larmor/cyclotron radiation will be present from accelerating charges. In the dynamic view I have taken in this work, is that the charges owe their radiation from coupling to the wall velocity, which, as it collapses, goes much faster than the speed of sound. This is what the new extra terms on the RHS of the following equation does:



    So what is it I am trying to achieve? Well hopefully it's clear, its about correcting the Reyleigh Plesset equation to suit the new physics we suspect.
    Last edited by Dubbelosix; 2018-Jun-02 at 08:54 PM.

  24. #24
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    Quote Originally Posted by Geo Kaplan View Post
    Again, the fact that you are still attempting to get first-year calculus correct tells us that you are not near ready to defend your idea. Perhaps you would consider working out the details first, rather than expecting a collaborative development here.
    No not at all, you came in here with a very arrogant attitude claiming the work was of highschool level. I really do challenge that. I don't think you understand how little the objection was concerning the log of the volume, while it is a completely dimensionless component and has no dimensional significance whatsoever.

    You came in here rude, it's our first meeting. Go figure. This isn't about defending the work, it's about you trying to insult me.

  25. #25
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    Quote Originally Posted by Dubbelosix View Post
    The equation does not work well though:

    ‘’Some have argued that the Rayleigh–Plesset equation described above is unreliable for predicting bubble temperatures and that actual temperatures in sonoluminescing systems can be far higher than 20,000 kelvins. Some research claims to have measured temperatures as high as 100,000 kelvins, and speculates temperatures could reach into the millions of kelvins. Temperatures this high could cause thermonuclear fusion.’’
    Can you provide a reference/link for this quotation?

  26. #26
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    Quote Originally Posted by Strange View Post
    Can you provide a reference/link for this quotation?

    sure: https://en.wikipedia.org/wiki/Sonoluminescence

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    I got the idea for the coupling of wall velocity to internal dynamics from my Friedmann cosmological studies. It is similar to how a hypothetical rotating Godel metric tends to drag matter around with it in the early stages of cosmology.

  28. #28
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    Quote Originally Posted by Geo Kaplan View Post
    Do you have an actual ATM idea that you are prepared to defend here? So far it seems that you are merely presenting a series of badly executed homework exercises. While no doubt thrilling to you, watching someone else work out first-year maths holds rather less interest for others.
    Quote Originally Posted by Dubbelosix View Post
    No not at all, you came in here with a very arrogant attitude claiming the work was of highschool level. I really do challenge that. I don't think you understand how little the objection was concerning the log of the volume, while it is a completely dimensionless component and has no dimensional significance whatsoever.

    You came in here rude, it's our first meeting. Go figure. This isn't about defending the work, it's about you trying to insult me.
    Both of you knock it off.

    Stop making assumptions about others motivations, stop with the veiled insults, and stop with calling out other members. If you have a problem with someone's post, you Report it, you do start in-thread arguments about it.

    If you keep it up, we'll start giving out infractions. Stick to math and physics, questions and answers.
    Last edited by Swift; 2018-Jun-03 at 03:36 AM. Reason: typo
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  29. #29
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    Quote Originally Posted by Dubbelosix View Post
    Heading in the right direction?

    Maybe you could be a gentlement and refresh that memory? You said I was heading in the right direction, so since I am almost there, why not be a bit more clear. It's not like you are harboring secrets.
    It is your derivation, with multiple errors. You seem to have found one of the errors. ATM is not the place for guiding you through calculus corrections, although we have started with avowed calculus illiterates and ended up with literates

    https://forum.cosmoquest.org/showthr...-x-y&p=1087190
    Quote Originally Posted by Dubbelosix View Post
    Did I forget something, let's see? Yes I did,



    Yes, but now you've misapplied that to your equation

    Quote Originally Posted by Dubbelosix View Post
    Also I would like to defend, there is nothing ''simple'' in what I have done. Just because it looks like I have used a simple algebra, does not take away the computation a person has to put in to make sure you are tracking dimensions. It takes study and an understanding of what you are doing to do this in the first place. I put intuition from my Friedmann studies to understand how to put in the pressure from Van der Waals forces and found a direct way to plug in equivalent terms for the radiation from cyclotron motion.
    Dimensional analysis is necessary but not sufficient. 1 meter doesn't equal 10 meters even though the dimensional analysis is balanced.

    Quote Originally Posted by Dubbelosix View Post
    I have explained what we are doing, I will explain it simpler - the Reyleigh Plesset equation describes the physics of an expanding and collapsing bubble. The equation does not work well though:

    ‘’Some have argued that the Rayleigh–Plesset equation described above is unreliable for predicting bubble temperatures and that actual temperatures in sonoluminescing systems can be far higher than 20,000 kelvins. Some research claims to have measured temperatures as high as 100,000 kelvins, and speculates temperatures could reach into the millions of kelvins. Temperatures this high could cause thermonuclear fusion.’’

    So we have a temperature gradient which is one unique change in our approach. Since magnetic field have been detected around the phenomenon, it's very likely Larmor/cyclotron radiation will be present from accelerating charges. In the dynamic view I have taken in this work, is that the charges owe their radiation from coupling to the wall velocity, which, as it collapses, goes much faster than the speed of sound. This is what the new extra terms on the RHS of the following equation does:



    So what is it I am trying to achieve? Well hopefully it's clear, its about correcting the Reyleigh Plesset equation to suit the new physics we suspect.
    But that's the same equation that I first quoted, right? Without any correction at all.

  30. #30
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    Quote Originally Posted by grapes View Post

    But that's the same equation that I first quoted, right? Without any correction at all.
    Yes, no correction. As for multiple errors, you'll need to defend this.

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