3 MARCO CONTEXTUAL.
NIVEL DE ESCOLARIDAD Y NUMERO DE HIJOS
3.3 PRESENTACION DE LOS HALLAZGOS
' V
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a tr n ts , th e c lr c u ln tion nnd th e su p e rflu id dens'^ty -'nd v e lo city * I d e i l l y v/o %'equlre^ to observe a s e r ie s o f Id e n tic a l hoat'^pulse trail'"
sloiitS ; to 8'mtch on a h ert current and observe th e eteed y d eflection ^ :md then to 3i^eid.mpo8o %t le as t one more heat p u lse and v e r ify th a t th e c ir c u la tion I s unchanged* / t t h is Idoal Is p a r tic u la r ly d i f f i c u l t to a ttain because any hoot current la rg e enough to giv e a monsur'ible steady d e fle c tion i s in e v ita b ly h ig h ly s u p e r c r itic a l (s e e beloYf) f the stead y d e fle c tion i s q u ick ly los t in g en era l turbu"- lence* S u p eipositlon o f a h eat p u lse on ly p r e c ip ita te s th e develop»* ment o f turbulence^ so th a t th e tr a n sie n t d e fle c tion due to the clrou»* la t lon cannot be ohedked a f t e r th e h eat current has been sw itched on#
Only one su c c e ssfu l comparison o f tr a n sie n t and stea d y d e fle c tion s has been made a t I t i s reproduced in fig u r e 7*4(a)g where the top tr a c e i s th e sig n a l from th e bob^ th e middle tra c e shows th e p u lse s and th e stea d y h eater vo lta g e , and th e sawtooth tra ce in d ic a te s seconds. H eater I I and fib r e H were used for t h i s comparison, which i s no t very so tis f a c tor y , for the c ir c u la tion had apparently sta r te d to decrease ju s t b efore th e h eat current was sw itched on. The i n i t i a l d e fle c tion
o f tho tr a n sie n ts ond th e steady d e fle c tion are in tho same d ir e c tion , as th ey should b e , and th e tr a n sie n t os c illa t ion v h ich aoooxnpanies th e s t a r t o f th e steady d e fle c tion i s a lso v i s i b l e . The stead y d e fle c tion i t s e l f la s t s for about a second u n t il the on set o f turb u len ce. The oir*» c u la tion deduced by equation (4,51 ) from th e las t tr a n sie n t b efore th e stead y h e it current i s
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V t r 0 « si « .f =
The c ir c u la tion deduced from the steady d e fle c tion , assuming th a t the su p e rflu id v e lo cit y p ro file i s f l a t , i s
V stea d y = °*5 " 0.1 cmanta Hence
y s te a d y / ^ tra n sien t ^ (/♦ 3 )
I f th e op tic a l a x is and th e a x is o f the tun n el are not ex a ctly p a r a lle l, p a it o f th e apparent tra n sv erse d e fle c tion o f the bob w i l l be
due to i t s dov;nsticam d e fle c tion by the normal f lu id , and so t his oom»»
p a ri son v /ill be in error* I t i s b e lie v e d tlia t the an gle betv/een the tviro axes i s not gr ea ter than 2 °, which would lead to a maximum error in th e measured, steady tra n sv erse d e fle c tion eq u ivalen t to about 0#1 quanta o f cir c u la tion at 1*3°K, end f a llin g to 0*02 quanta au
That tho misallgnmont i s c e r ta in ly no w oise than t n is i s confiim ed by the f a c t th a t noim ally no steady d e fle c tion i s d e te c ta b le whun a la rg e heat current i s sw itch ed on a t 1 and th a t th ere i s no response d etected to th e m ajority o f heat p u ls e s .
(a) frequency 3 " 2- - 1 - L ,..a i ■I 11 ■I I I i I I I 11 I I I ■«— ,1.
I
i
* «-.2
-'1 2 *3 Y q u a n ta frequency (b) L A I I : 6 5 A 3 2 1 + i 1 li t i t J I I I Ê m Ê Ê I I i J— » "•3 -'2 -*1 0 2 *3 y quanta Figure 7. 5. H i s to gr a m s of p e r s i s t e n t c i r c u l a t ion s at 1*3*^K (a) with heater I and fib r e I ;(85)
heliwjii ( a p a r t from (iis tu rb a a c e due to th e p u ls e s th em selv es) th e re may bo no dotoctablc oiroulation about the fib r e for long perioûa* /! email
oli"culation w ill eventually appear and gradually groiv, aometlmee
decaying again, but often attaining a la ig e value which then p e r sists
..ith some variation thiough perhaps twenty pulses or, i f the p ulses are
intem%)te<i, for a minute or more ^vitiiout p u lses, before gradually
decaying. y,part from th eir persisten ce the most strik in g aspeoL of the
observed circu lation s i s th eir d irection al bias: almost a l l are in the
positiv e d irection , corresponding, that i s , to clock\,'d.se oiroulation
about the fib re (vie'/zed from above)# The only exceptions occurred soon a fte r a steady heat current in the tunnel.
C irculations which remain above o f th eir maximum value for
more than th ir ty seconds are judged to be p articu larly p ei'sisten t,
histogram o f the f^parent oiroulation deduood from the largest tran»»
sien t d eflection attained by such oircu lation s i s given in figure 7*5(&)«
Some re su lts obtained during very low, steady heat ourrents are also
included on th is histogram (see Section (o) below). The longest time
for -\,iiiich a oiroulation has been observed to p ei'sist at above half*"
maxlmuia i s four and three quarter minutes.
There i s a possib le system atic error in the resu lts of up to
perhaps 25/^, due to inaccurate calibration of the recording uyatom and
error in the weight of the nylon bob, wliile variation in the s e n s itiv ity
of tho system during the zun lends to a random error of about 1C%r,.
i n s t a b i l i t y i n th e le n g th and h e ig h t o f th e p u ls e s . The sp re a d of th e
values of y within the maximum o f the histogram is therefore hardly
sig n ific a n t, and we may suppose that th e r e i s a s in g le p a r t i c u l a r l y
p ersisten t circu la tion , o f apparent s is e
V <= (
0 . 2 3“ 0.01 ) quanta,
(7-4)
th e mean o f th e maximum o f the h isto g ram . There i s an in d ic a tio n th a t Y K -0 ,2 3 quanta may a ls o b e p e r s i s t e n t , once i t h as been e s ta b lis h e d
against the general bias* The value y » 0*12 quanta i s perhaps a sport,
A lthougli i t does n o t appear a s such on the h isto g ra m , zero circu la tion i s a ls o a p a r t i c u l a r l y s ta b le value, No circu la tion , p ersisten t
or non-persistent, larger than the la ig e st shown on the histogram has
been observed with f i b r e I end h e a te r I ,
With fib re I I and h e a te r IX sim ilar r e s u l t s have been o b ta in e d a t
1,3°K, The p ersisten ce o f circu la tion s i s not quite so maiked, and
th eir b ia s i s in th e opposite d ir e c tio n . C irc u la tio n s o f o p p o s ite se n se to th e g e n e ra l b ia s in u n d is tu rb e d helium a g a in occur a f t e r ste a d y h e a t
ourrents* A histogram o f th e maximum v a lu e a tta in e d by circu la tion s
w hich rem ained above 50^ o f th eir maximum f o r t h i r t y seconds or more i s
. shown in f ig u r e 7»3(b)* This criterion for persisten ce ( s l i g h t l y l e s s
stringent than that used with fib re 1 and heater l ) i s not id e a l,
although sim p le to apply, for some o f the circu lation s sa tisfy in g i t
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b o th sauBOs grow and decay very sm oothly, but do n o t p e r s is t lo n g enough
to s a t i s f y th e c rite rio n ® N e v e rth e le s s no c ir c u la tio n la r g e r th a n th e la r g e s t on th e h isto g ra m h as been observed. With t h i s fib r e and h e a te r th e lo n g e s t tim e for w hich a c ir c u la t io n remained above h a lf -maximum was two m in u tes.
A p art from th e change o f s ig n , th e d if f e r e n c e betw een th e mean v a lu e o f th e maximum o f this h isto g ram
y = - ( O .i? - 0*01 ) q u a n ta , (7*5)
and th a t o f th e p re v io u s one (e q u a tio n (7* 4)) i s not s i g n i f i c a n t , as i t co u ld be due to e r r o r s in c a lib r a tion and in th e w eig h ts o f th e nylo n bobs on fib r e s I and I I ,
( i i i ) S t a b i l i t y and p e r s is te n c e o f c ir c u la tio n .
To f a c i l i t a t e comparison betw een r e s u l ts in d iffe r e n t c o n d itio n s a s in g le number i s re q u ire d to ex p re ss th e s t a b i l i t y and p e r s is te n c e o f c irc u la tio n ® Such a s t a t i s t i c sh o u ld p refera b ly be in d ep en d en t o f th e av erag e m agnitude and b ia s o f th e c ir c u la t io n , re a so n a b ly s ta b le in g iv en c o n d itio n s , and easy to c a lc u la te * I t should n o t b e to o much a f f e c te d b y th e f a c t t h a t sm all c ir c u la tio n s a re l o s t in th e n o ise* A s u ita b le
where i s th e p ealc-to -p eak d e fle c tion o f th e n th tr a n sie n t (w ith appropriate s ig n ). Equation (7*6) i s a s lig h t ly modified s e r ia l
cor r e la tion co e f fic ie n t w ith la g one (H oel 1954, p . 255)# In th e u s u a l form o f t h is c o e f f ic ie n t the would be m easured from t h e ir mean
v a lu e , but in th e p resen t ca se th e r e i s a known tru e g e ro , and we wish th e r e s u lts to be u n a ffected by b ia s about t hi s zero . The m odified