From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Subject: Re: Responses to Dale Bass
Organization: University of Virginia
Date: Fri, 8 Jan 1993 02:12:10 GMT

In article <1993Jan7.234826.23344@asl.dl.nec.com> terry@asl.dl.nec.com writes:
>Hi folks,
>
>In article <1993Jan7.182337.19186@murdoch.acc.Virginia.EDU>
>crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
>
>> In article <1993Jan7.080252.15953@asl.dl.nec.com>
>> terry@asl.dl.nec.com writes:
>> 
>> | I was interested mainly in _very_ thin shock wave media, not the
>> | conventional thick stuff...
>>
>> Why the 'thick' vs. 'thin' stuff?  A shock is a shock.  They are usually
>> pretty thin.  A vacuum bubble collapsing does not necessarily create a
>> shock, it is also not necessarily energetic.
>
>
>Assume the following (highly non-equlibrium) initial conditions:
>
>  (1) A very sharp, gaseous "bubble boundary" with a high degree of
>      spherical symmetry,
>
>  (2) A bubble interior that is an extremely hard vacuum, and
>
>  (3) An initial velocity profile in which the gaseous surface is moving
>      radially inward at a even rate either equal to, or in excess of,
>      the velocity of sound in that gas under those surface conditions.
>
>
>First question:  _Do_ you call this a "shock wave," or not?  I have
>always understood a shock wave to be a result of pushing an object
>through another media at a rate beyond its normal sonic velocity.

      Not exactly, there would be a rarefaction wave within
      the fluid.  Some people call your surface a 'contact wave'.
      However, you are still limited in driving force
      to the ambient pressure.  Shock tubes are run somewhat this way, but
      you don't obtain fusion.
       
      One can do an analysis of this collapse (an empty bubble as
      per Rayleigh), but it breaks down at the time compressibility
      effects start to become important (and starts to impede the
      acceleration process).

      An even better way, though, to get the fluid to higher 
      thermal energy is to assume a spherical piston of some sort in a gas.
      Give the 'piston' a massive whang, and a strong shock is created.
      As the center is approched, the shock itself gets stronger.
      One can solve this using similarity methods (c.f. Landau and Lifshitz,
      Fluid Mechanics, section 107). As the center of the the region 
      approches, the energy within the shock goes as 

                    E ~ R^{5-2/a}

      Where $a$ is a similarity parameter (about 0.7 for polytropic 
      gases with with gamma = 5/3 (monatomic) or gamma = 7/5 (diatomic).

      So, you can see that though the shock itself gets stronger, the
      energy it contains the decreases drastically as one approaches
      the center.

>Second question:  Will the inboud surface velocity of the whatever-you-
>choose-to-call-it of my hypothetical scenario:
>
>  (a) Always rapidly slow down
>
>  (b) Sometimes remain at the same velocity
>
>  (c) Sometimes accelerate rapidly
>

     Look at this another way.  The inbound surface increases its
     velocity.  The velocity is limited by a) real gas effects
     b) energy.  If you have sufficient energy, you have 
     a thermonuclear weapon.  And even if you figure out a way 
     to simply extract some tail of the standard energy distribution
     (without violating the laws of thermodynamics),
     you have to go way way up the tail to get to fusion energies.
     One has to go so far up the tail that there are probably
     no such molecules actually present in the fluid, and you
     cannot get the fluid to give them to by itself you without violating
     the second law.

>The ones that "win" _must_ be accelerated to some degree relative to the
>ones that "lose," else the competition cannot be resolved.  If there is
>enough diversity of inward momentum, such a "competition" will be resolved
>trivially by selection of the faster components (already a violation of
>your second law concerns, of course, but please don't forget Hilsche (sp?)
>vortex tubes).

     There is a way to quantify this gain in velocity, but it is not
     in the thermodynamically organized fashion presented.  However,
     my specific second law objection was to a specific scheme.  I 
     do have general second law objections, but it seems silly to bring 
     them up in the absence of some quantification.

>If there is not enough diversity of the momentum profiles, I say that you
>_will_ get an acceleration effect as in (c), whatever you wish to call it.
>I call it wedge-out, and I maintain (as originally in the UC draft) that
>this effect is _quantitatively_ different from milder effects such as a
>"classic" shock wave in which such a "competition" does not exist -- there
>will never be any of the original matter making it to the center.

     It doesn't matter.  There will certainly be acceleration, but
     pressure-limited, and nothing truly exciting for ordinary fluids
     under ordinary conditions.
>
>P.S. -- Dieter; thanks; yes, words are dangerous.  (And so are equations
>        when they lack common sense and good analysis to back them up!)
>
>	But I've nailed one or two items with this style of information-based,
>        "search space" theorizing (e.g., the prediction of hydrogen forming
>        atomic bands in metals), and I'm starting to get a bit more stubborn
>	about it having some real value as an approach to physical problems.

      Words are much more dangerous than equations.  Equations are 
      well-defined and can be examined quantititively for correlations
      with experience.  Words are fluid and mutable and ill-defined.

                              dale bass


                          

-- 
C. R. Bass                                          crb7q@virginia.edu        
Department of Wildebeest
Transvaal                                           (804) 924-7926
Newsgroups: sci.physics.fusion