Sergio P. Ratti - University of Pavia – Vienna, april 17° 2008Sergio P. Ratti - University of Pavia – Vienna, april 17° 2008

Sergio P. Ratti - University of Pavia – Vienna, april 17° 2008Sergio P. Ratti - University of Pavia – Vienna, april 17° 2008

Wherever it gets multiscale, complexityWherever it gets multiscale, complexity comes out from behindcomes out from behind

OR RATHEROR RATHER

Wherever it gets complex, Wherever it gets complex, (or complicated…), multiscale (or complicated…), multiscale

comes out from behindcomes out from behind

Complexity has several different meanings Complexity has several different meanings in different scientific contexts.in different scientific contexts.

Equivalently, the “multiscale” features were Equivalently, the “multiscale” features were not always immediately discovered in several not always immediately discovered in several fields of research although they were clearly fields of research although they were clearly

(a posteriori!) (a posteriori!) hidden inside the data.hidden inside the data.

The treatment of non linear phenomena and The treatment of non linear phenomena and extreme events received a strong push by the extreme events received a strong push by the

use of the fractal approach,to geometry as well use of the fractal approach,to geometry as well as to probability distributions, during the lastas to probability distributions, during the last

3 decades of last Century.3 decades of last Century.

a)-most meteorologists used Tchebychev a)-most meteorologists used Tchebychev Polynomials to simulate clouds and to Polynomials to simulate clouds and to interpolate rainfall intensity.interpolate rainfall intensity.

Till about the early seventies:Till about the early seventies:

b)-Cosmologists were in trouble to tackle the b)-Cosmologists were in trouble to tackle the problem of the large scale distribution of matterproblem of the large scale distribution of matterin the Universe. They were bound (and some still are) in the Universe. They were bound (and some still are) to the to the “cosmological principle” “cosmological principle” that implies a local that implies a local isotropy, which in turn, assuming analyticity of the isotropy, which in turn, assuming analyticity of the mathematical solutions brings directly to the mathematical solutions brings directly to the assumption of homegeneous distribution of matter assumption of homegeneous distribution of matter in the Universein the Universe

c)- elementary c)- elementary particle physicists particle physicists didn’t even know didn’t even know of the existence of of the existence of fractals. Gabriele fractals. Gabriele Veneziano in the Veneziano in the 90’s,90’s,at an International at an International Conference said: Conference said: ““the production of the production of particle jets looks particle jets looks like the production like the production of objects known of objects known in geometry by the in geometry by the name of fractals”name of fractals”

H.E. multiparticleH.E. multiparticleproductionproduction

e)- almost nobody knew that the Lorenze)- almost nobody knew that the Lorenzattractor had fractal dimension of about attractor had fractal dimension of about 2.0.2.0.Therefore statistical mechanics was moving Therefore statistical mechanics was moving along its own directions in dealing with chaos.along its own directions in dealing with chaos.

d) Complexity meant solving the problem of d) Complexity meant solving the problem of tritium i.e. a three body problem (long lasting tritium i.e. a three body problem (long lasting debates among nuclear theorists)debates among nuclear theorists)

f) Economists were far, far away from any f) Economists were far, far away from any use of fractals in dealing with stock marketuse of fractals in dealing with stock market

h) Genetists couldn’t think of possible h) Genetists couldn’t think of possible multi-multi-fractal properties of genomic fractal properties of genomic sequences, nor sequences, nor cardiologists could think of the cardiologists could think of the intermittency intermittency phenomena in the variability of human phenomena in the variability of human heartbeat dynamics.heartbeat dynamics.

g) Physics of matter was struggling like hellg) Physics of matter was struggling like hellto tackle the phase transitions phenomenato tackle the phase transitions phenomena

Fractal descriptionFractal description of of TWOTWO ecologicalecological

DISASTERSDISASTERS

Fractal descriptionFractal description of of TWOTWO ecologicalecological

DISASTERSDISASTERS

Sergio P. Ratti - University of Pavia - AGU- Montreal may 2004Sergio P. Ratti - University of Pavia - AGU- Montreal may 2004

Here’s what was demolished after the accidentHere’s what was demolished after the accidentin Sevesoin Seveso

Here’s what was demolished after the accidentHere’s what was demolished after the accidentin Sevesoin Seveso

7-7-1976: ICMESAICMESA factory: italian branch of

GIVAUDAN GIVAUDAN (Hoffman La Roche)(Hoffman La Roche) production of herbicides

CHEMICAL REACTOR EXPLODEDCHEMICAL REACTOR EXPLODEDspread a cloud of supertoxic material

TTETRAETRACCHLORO-HLORO-DDI-BENZO-p-I-BENZO-p-DDIOXINIOXIN

TCDD or DIOXINTCDD or DIOXIN

VERYVERY SIMMETRIC AND SIMMETRIC AND

VERYVERY STABLE STABLE

COMPOUNDCOMPOUNDVERY HARDVERY HARD

TO GET RID OF TO GET RID OF IT !!!IT !!!

VERYVERY SIMMETRIC AND SIMMETRIC AND

VERYVERY STABLE STABLE

COMPOUNDCOMPOUNDVERY HARDVERY HARD

TO GET RID OF TO GET RID OF IT !!!IT !!!

THIS IS WHAT WAS FOUND IMMEDIATELY AFTERTHIS IS WHAT WAS FOUND IMMEDIATELY AFTERIN CHERNOBYLIN CHERNOBYL

THIS IS WHAT WAS FOUND IMMEDIATELY AFTERTHIS IS WHAT WAS FOUND IMMEDIATELY AFTERIN CHERNOBYLIN CHERNOBYL

In the village of In the village of LENEVLENEV , 19 km leewards , 19 km leewardsfrom Chernobyl:from Chernobyl:

in the in the thyroid of childrensthyroid of childrens over over 250 rem of 250 rem of 131131I measuredI measured; ;

average dose in townaverage dose in town 25 mrem/ hour25 mrem/ hour..

In the village of In the village of LENEVLENEV , 19 km leewards , 19 km leewardsfrom Chernobyl:from Chernobyl:

in the in the thyroid of childrensthyroid of childrens over over 250 rem of 250 rem of 131131I measuredI measured; ;

average dose in townaverage dose in town 25 mrem/ hour25 mrem/ hour..

Inhabitants of Inhabitants of PRYPIATPRYPIAT township township(3 km from Chernobyl)(3 km from Chernobyl)

protected by concrete buildings, protected by concrete buildings, inhaled inhaled much smaller dosesmuch smaller doses

Inhabitants of Inhabitants of PRYPIATPRYPIAT township township(3 km from Chernobyl)(3 km from Chernobyl)

protected by concrete buildings, protected by concrete buildings, inhaled inhaled much smaller dosesmuch smaller doses

In the major town of KIEVIn the major town of KIEVestimated an average dose ofestimated an average dose of

0.5 - 0.8 mrem/hour0.5 - 0.8 mrem/hour

In the major town of KIEVIn the major town of KIEVestimated an average dose ofestimated an average dose of

0.5 - 0.8 mrem/hour0.5 - 0.8 mrem/hour

Dangerous threshold for humans: 50 rem/yDangerous threshold for humans: 50 rem/yDangerous threshold for humans: 50 rem/yDangerous threshold for humans: 50 rem/y

DIFFERENCESDIFFERENCESDIFFERENCESDIFFERENCES• SEVESOSEVESO

• TCDD: a TCDD: a substancesubstance!!

• areaarea: 4 km x 7 km, : 4 km x 7 km, microclimatemicroclimate;;

• only only one one substance;substance;• material: TCDD, material: TCDD, heavy heavy

moleculesmolecules;;

• lowlow altitude; altitude;

• smallsmall scale. scale.

• SEVESOSEVESO• TCDD: a TCDD: a

substancesubstance!!

• areaarea: 4 km x 7 km, : 4 km x 7 km, microclimatemicroclimate;;

• only only one one substance;substance;• material: TCDD, material: TCDD, heavy heavy

moleculesmolecules;;

• lowlow altitude; altitude;

• smallsmall scale. scale.

• CHERNOBYLCHERNOBYL• RADIOACTIVITY: aRADIOACTIVITY: a• phenomenonphenomenon!!!!• areaarea: thousands of km: thousands of km22

macroclimatemacroclimate;;• manymany nuclides; nuclides;• material: material: mostlymostly inorganic inorganic

chemical elements;chemical elements;

• highhigh altitude; altitude;

• largelarge scale. scale.

• CHERNOBYLCHERNOBYL• RADIOACTIVITY: aRADIOACTIVITY: a• phenomenonphenomenon!!!!• areaarea: thousands of km: thousands of km22

macroclimatemacroclimate;;• manymany nuclides; nuclides;• material: material: mostlymostly inorganic inorganic

chemical elements;chemical elements;

• highhigh altitude; altitude;

• largelarge scale. scale.

APPLICATION OF FRACTALS TO TWO VERY DIFFERENT SITUATIONS

Distance Chernobyl-Italy over 3000 km

Maximum distance in Seveso below 10 km

SEVERAL MEASURING CAMPAIGNSSEVERAL MEASURING CAMPAIGNSwith different measuring procedureswith different measuring procedures

FROM 1976 TO 1984FROM 1976 TO 1984IN ALL ZONES: A,B,RIN ALL ZONES: A,B,R

SEVERAL MEASURING CAMPAIGNSSEVERAL MEASURING CAMPAIGNSwith different measuring procedureswith different measuring procedures

FROM 1976 TO 1984FROM 1976 TO 1984IN ALL ZONES: A,B,RIN ALL ZONES: A,B,R

1976/77

zone A431 meas.zone B+R

718 meas.

ICMESA

MANY NAT’L AGENCIESMANY NAT’L AGENCIESplus any kind of subjectplus any kind of subjectmeasuring radioactivitymeasuring radioactivity

(not all usefull…)(not all usefull…)

MANY NAT’L AGENCIESMANY NAT’L AGENCIESplus any kind of subjectplus any kind of subjectmeasuring radioactivitymeasuring radioactivity

(not all usefull…)(not all usefull…)

CHERNOBYL SEVESO

Lombardy: Lombardy: located in northern Italylocated in northern Italy

Seveso:Seveso: Town half way betweenTown half way between

Milano and ComoMilano and Como

DATA QUALITYDATA QUALITY

• SEVESOSEVESO• density in density in g/mg/m22

• material: TCDD, material: TCDD, heavy heavy moleculesmolecules;;

• measurementsmeasurements: mostly : mostly done by ONE lab. done by ONE lab. complicated complicated methodmethod;;

• unknown accuracyunknown accuracy;;

• several several NVNV=no =no value measurablevalue measurable;;

• CHERNOBYLCHERNOBYL• Bq/mBq/m2 2 or or Bq/kgBq/kg

• material: most material: most inorganicinorganic nuclidesnuclides;;

• measurementsmeasurements: all sort of : all sort of labs. labs. both excellent both excellent and mediocreand mediocre;;

• unknown calibrationsunknown calibrations;;

• location location badly known, badly known, geographically sparsegeographically sparse

SEVESOSEVESO

Samples were taken Samples were taken accordingaccordingto prepared grids.to prepared grids.

The The measurements were measurements were aatotal of :total of :10781078 in the 1976/77 in the 1976/77 camp.camp.31203120 in the 1980/81 in the 1980/81 camp.camp.

Variations over 4 o. of Variations over 4 o. of m.m.Many NV (no value) Many NV (no value) meas.meas.

Remeasuring campaignsRemeasuring campaignswere organizedwere organized

SEVESOSEVESO

Samples were taken Samples were taken accordingaccordingto prepared grids.to prepared grids.

The The measurements were measurements were aatotal of :total of :10781078 in the 1976/77 in the 1976/77 camp.camp.31203120 in the 1980/81 in the 1980/81 camp.camp.

Variations over 4 o. of Variations over 4 o. of m.m.Many NV (no value) Many NV (no value) meas.meas.

Remeasuring campaignsRemeasuring campaignswere organizedwere organized

The problem of the The problem of the NVNVmeasurements was measurements was

a a serious serious oneone from thefrom thestatistical point of viewstatistical point of view

The problem of the The problem of the NVNVmeasurements was measurements was

a a serious serious oneone from thefrom thestatistical point of viewstatistical point of view

Emergency analysisEmergency analysisEmergency analysisEmergency analysis

FIRST THING: make a FIRST THING: make a survey with “level survey with “level curves”curves”

FIRST THING: make a FIRST THING: make a survey with “level survey with “level curves”curves”

OBSERVE:OBSERVE:1: region of area about1: region of area about 5 km x 7 km5 km x 7 km overall overall2- several regions have 2- several regions have NONO measurements; measurements;3- rather wild 3- rather wild fluctuationsfluctuations;;4- 4- need ofneed of interpolationinterpolation of data in some regions.of data in some regions.

OBSERVE:OBSERVE:1: region of area about1: region of area about 5 km x 7 km5 km x 7 km overall overall2- several regions have 2- several regions have NONO measurements; measurements;3- rather wild 3- rather wild fluctuationsfluctuations;;4- 4- need ofneed of interpolationinterpolation of data in some regions.of data in some regions.

Very clear fractalVery clear fractalcharacterscharacters

Very clear fractalVery clear fractalcharacterscharacters

1st FRACTAL ANALYSIS1st FRACTAL ANALYSIS1st FRACTAL ANALYSIS1st FRACTAL ANALYSIS

1- Use both campaigns;1- Use both campaigns; (1976/77 and 1980/81)(1976/77 and 1980/81)2- Measure fractal D of 2- Measure fractal D of the two samples:the two samples: (A) and (A+B+R)(A) and (A+B+R)

1- Use both campaigns;1- Use both campaigns; (1976/77 and 1980/81)(1976/77 and 1980/81)2- Measure fractal D of 2- Measure fractal D of the two samples:the two samples: (A) and (A+B+R)(A) and (A+B+R)

DDAA = = 1.691.69248248

DDABRABR = = 1.691.69498498

DDAA = = 1.691.69248248

DDABRABR = = 1.691.69498498

Very modest scale factor: Very modest scale factor: Surface ratioSurface ratio=17.87/.835=21.4=17.87/.835=21.4

Very modest scale factor: Very modest scale factor: Surface ratioSurface ratio=17.87/.835=21.4=17.87/.835=21.4

logK(r)

logK(r)

log r

log r

ZONE A

ZONE A+B+R

More realistic activity in the FRACTAL simulation!More realistic activity in the FRACTAL simulation!More realistic activity in the FRACTAL simulation!More realistic activity in the FRACTAL simulation!

Plus few othersPlus few others

AIR CONCENTRATION IN ITALYGEOGRAPHICAL DISTRIBUTION

OF THE MEASUREMENTS PER NUCLIDE

AIR CONCENTRATION IN ITALYGEOGRAPHICAL DISTRIBUTION

OF THE MEASUREMENTS PER NUCLIDECHERNOBYLCHERNOBYLCHERNOBYLCHERNOBYL

North-Italy North-Italy 133,000 km133,000 km22

1164 data 1164 data +240+240 recovered recovered1404 “measur.”1404 “measur.”

A set of 10 Levy flights

55

66

77

88

99

1010

1111

C()

C()

commentscommentscommentscomments

The phenomenonis a stochastic

process:

=.35-.52=.35-.52

The codimensionof the averagefield is around

CC11=1.0=1.0

The phenomenonis a stochastic

process:

=.35-.52=.35-.52

The codimensionof the averagefield is around

CC11=1.0=1.0

Universal Multifractals and SEVESOUniversal Multifractals and SEVESOUniversal Multifractals and SEVESOUniversal Multifractals and SEVESO

1108 soil Cs contamination1108 soil Cs contamination104 soil Cs contamination104 soil Cs contamination

Several Countries give very similar Several Countries give very similar resultsresults

(Germany, Poland + others)(Germany, Poland + others)

Several Countries give very similar Several Countries give very similar resultsresults

(Germany, Poland + others)(Germany, Poland + others)

Universal Multifractals and CHERNOBYLUniversal Multifractals and CHERNOBYLUniversal Multifractals and CHERNOBYLUniversal Multifractals and CHERNOBYL

Asymptotic behaviourqD=2,2

Asymptotic behaviourqD=2,2

137Cs in 148 towns around Chernobyl (r<100km)137Cs in 148 towns around Chernobyl (r<100km)

ANALYSIS BY THE PARIS GROUP: D. Schertzer et al.ANALYSIS BY THE PARIS GROUP: D. Schertzer et al.

~~ 1.5, C 1.5, C11 ~~ 0.4 0.4ANALYSIS BY THE PARIS GROUP: D. Schertzer et al.ANALYSIS BY THE PARIS GROUP: D. Schertzer et al.

~~ 1.5, C 1.5, C11 ~~ 0.4 0.4

CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS

Seveso zone A: 5 kmx7 km = 35 km2; A+B+R ~ 102 km2;

North Italy area ~ 104 km2

Chernobyl area ~ 107 km2;

Seveso zone A: 5 kmx7 km = 35 km2; A+B+R ~ 102 km2;

North Italy area ~ 104 km2

Chernobyl area ~ 107 km2;

PollutionPollution inhomogeneity inhomogeneity clearclear in all cases: in all cases:ScalingScaling features are well features are well presentpresent

PProb. rob. DDistr. istr. MMult. ult. SScaling in both cases.caling in both cases.UNIVERSAL MULTIFRACTALSUNIVERSAL MULTIFRACTALS

Seveso:~~ 0.4 0.4, , CC11 ~~ 1.0 1.0,, rainfall !!

Chernobyl: ~~ 1.5, C 1.5, C11 ~~ 0.4 0.4 clouds !!

PollutionPollution inhomogeneity inhomogeneity clearclear in all cases: in all cases:ScalingScaling features are well features are well presentpresent

PProb. rob. DDistr. istr. MMult. ult. SScaling in both cases.caling in both cases.UNIVERSAL MULTIFRACTALSUNIVERSAL MULTIFRACTALS

Seveso:~~ 0.4 0.4, , CC11 ~~ 1.0 1.0,, rainfall !!

Chernobyl: ~~ 1.5, C 1.5, C11 ~~ 0.4 0.4 clouds !!

Let’s move to High Energy PhysicsLet’s move to High Energy Physics

In HEP scaling came about in the early 60’s In HEP scaling came about in the early 60’s in a purely empirical way: called KOBA, in a purely empirical way: called KOBA,

NIELSEN OLESEN scaling law. It was NIELSEN OLESEN scaling law. It was related simply to empirical scaling of the related simply to empirical scaling of the

normalized charge multiplicity normalized charge multiplicity distributionsdistributions

Only rarely we can “measure” neutral particles; Only rarely we can “measure” neutral particles; only rarely we can distinguish eonly rarely we can distinguish eK,p. K,p. We can detect only the electric chargeWe can detect only the electric charge

a + b ∑a + b ∑11

nn c cii ; n=2,4,6,8,……… ; n=2,4,6,8,………

KNO make the hypothesis that at high energy the KNO make the hypothesis that at high energy the proba- bility distributions Pproba- bility distributions P

nn for detecting n final for detecting n final

particles exhi- bit a simple scaling law with particles exhi- bit a simple scaling law with (n/<n>) universal function(n/<n>) universal function

PPnn = 1/<n> = 1/<n> (n/<n>)(n/<n>)But in the early 80’s the observation of “singleBut in the early 80’s the observation of “singleevents” events” (in diffe-(in diffe-rent experiments)rent experiments)showed anomalousshowed anomalousfluctuations in thefluctuations in thedistribution of thedistribution of theproduction angles!!production angles!!

The variables are…..The variables are…..techinalities !!!!techinalities !!!! Intermittency!!!!Intermittency!!!!

Let’s get rid of the technicalities once Let’s get rid of the technicalities once for all!!for all!!

rapidity y=tanhrapidity y=tanh

-1-1

pseudorapidity pseudorapidity =-ln(tan =-ln(tan /2)/2)

Two dimensionless variables linked to the Two dimensionless variables linked to the production angle production angle or to the relativistic or to the relativistic

velocityvelocity of the final particlesof the final particles

y y when when 1 1

=v/c=v/c

Elementary particle physicists are the most Elementary particle physicists are the most reductionists of the scientists: 6 leptons; 6reductionists of the scientists: 6 leptons; 6

quarks, 8 gluons, 2 vector mesons, 1 photon,quarks, 8 gluons, 2 vector mesons, 1 photon,6 angles for Cabibbo Kobayashi Maskawa6 angles for Cabibbo Kobayashi Maskawa

(CKM matrix) (CKM matrix)

How can How can we we

produ-produ-ce n ce n finalfinal

particlesparticles??

PartonPartonShower !Shower !

!!!!!!

Parton shower? A simple Parton shower? A simple binarybinary

multiplicative cascade multiplicative cascade process!!!process!!!

therefore we can check a variety of therefore we can check a variety of frac-frac-al features:al features:-- the Lipshitz-Holder coefficient; the Lipshitz-Holder coefficient;--Probab. Distrib. Multiple Scaling Probab. Distrib. Multiple Scaling (no)(no)-Universal Multifractal parameters: -Universal Multifractal parameters: CC11,,

therefore we can check a variety of therefore we can check a variety of frac-frac-al features:al features:-- the Lipshitz-Holder coefficient; the Lipshitz-Holder coefficient;--Probab. Distrib. Multiple Scaling Probab. Distrib. Multiple Scaling (no)(no)-Universal Multifractal parameters: -Universal Multifractal parameters: CC11,,

hadronization and hadronization and conservation laws conservation laws cannot hidecannot hide

the basic properties of the the basic properties of the cascade process!!!!!cascade process!!!!!

Since for n produced particles:Since for n produced particles:

PPoo= ∑= ∑11

nn PPcici ; E ; Eoo+m+mtargettarget= ∑= ∑

11

nn E Ecici

there are “annoying” limitationsthere are “annoying” limitations::1- “i” is a 1- “i” is a discrete variablediscrete variable2- energy and momentum 2- energy and momentum conservation conservation confines the value of the last confines the value of the last particle,particle,3- 3- big numbers are nothing big numbers are nothing compared to compared to the number of molecules in a the number of molecules in a mole!!mole!!

More: More: binwidthbinwidth limited by experimental re- limited by experimental re-solution; the number of steps in the cascade solution; the number of steps in the cascade can’t go too high; can’t go too high; can’t go too close to 0! can’t go too close to 0!

Analises are done using either Analises are done using either generalised generalised statistical momentsstatistical moments::

GGq q ((y) y) ≈≈ ( (y)y)––(q)(q) or or factorial factorial momentsmoments::

FFqqVV((y) = 1/M {∑y) = 1/M {∑MM

m=1 m=1 [<n[<nmm(n(nmm-1)…(n-1)…(nmm-q+1)>]/(n-q+1)>]/(nmm))qq>}>}

oror

FFqqHH((y) = 1/M {∑y) = 1/M {∑MM

m=1 m=1 [<n[<nmm(n(nmm-1)…(n-1)…(nmm-q+1)>]/(-q+1)>]/(<<nnmm>>))qq}}

<n<nmm>=<n>/M = ∑>=<n>/M = ∑m m nnmm/M/M

Called HorizontalCalled Horizontal

Called VerticalCalled Vertical

NOW: divide the y,NOW: divide the y, interval into interval intodecreasing bins. After n steps (width decreasing bins. After n steps (width ), ),

any subset S(any subset S() has a d-dimension ) has a d-dimension MMdd[S([S()])]

with with =k/M=k/M; ; k=0,1,2,3,.,Mk=0,1,2,3,.,M; k bin sequence:; k bin sequence:

MMdd[S([S()]=N)]=Nnn(() ) dd

This brings to the Lipshitz-Holder form: d=f(This brings to the Lipshitz-Holder form: d=f() )

f(f()=-[)=-[ln ln +(1- +(1-)ln(1-)ln(1-)]/ln2 and)]/ln2 and== M Mdd[x([x()+)+]-M]-Mdd[x([x()]=)]=

is the Lipshitz-Holder coefficientis the Lipshitz-Holder coefficient

Plot f(Plot f() instead of f() instead of f())

In an histogram of N points with NIn an histogram of N points with Nii points in points in cell i,cell i,

we build the mass coefficients we build the mass coefficients ii=N=Nii/N and the /N and the q-th q-th

statistical momentstatistical moment M Mdd (q (q)=)=iiq q dd= N(q= N(q) ) d d

that is:that is:N(qN(q)=)=ii

q q ˜̃

––(q) (q) that leads tothat leads to

MMdd(q(q)≈)≈ qq(q)-f[(q)-f[(q)]+d(q)]+d

that for that for 0 and d= 0 and d=(q) implies(q) implies

qq=f(=f(qq)-q)-qqq; ; qq=d=dqq/dq/dq

We can measure experimentally We can measure experimentally (q) for(q) fordifferent values of the bin different values of the bin and getand get

f[f[(q)] or viceversa(q)] or viceversa

xxat 150 GeV/cat 150 GeV/c; exp. at ; exp. at FermilabFermilab

pppp Inclusive reaction: 5 different beams all together.Inclusive reaction: 5 different beams all together.

X means anything; for us from 6 to 22 charged particlesX means anything; for us from 6 to 22 charged particles

q

Using Universal Multifractals Double Trace Moments Using Universal Multifractals Double Trace Moments DTM:DTM:

<<qq>=>=K(q) K(q) K(q) = moments’ scaling functionK(q) = moments’ scaling function

┌┌= C= C11 (q (q-q)/(-q)/(-1) if -1) if ≠1≠1

DTM: K(q,DTM: K(q,)= )= K(q) where K(q)=│ K(q) where K(q)=│ └ └= C= C11qlnqqlnq if if =1=1

we determine we determine for each seminclusive collisions, for each seminclusive collisions, for for 66

values of values of andand for 6,for 6,88,…,,…,1212,…,,…,1818,…,22 prongs,…,22 prongs

(N(Nchch)=1-1/(1+a√N)=1-1/(1+a√Nchch+bN+bNchch); );

(N(Nchch)=a’√N)=a’√Nch ch +b’N+b’Nch ch ; ;

From the plot, From the plot, at our at our energyenergy, we can’t decide , we can’t decide

whether whether or not or not overcomes 1. overcomes 1.

Thus we can’t conclude if Thus we can’t conclude if the the

parton shower can becomeparton shower can become(or is) a hard process!!(or is) a hard process!!

If we plot If we plot vs. charge multiplicity of the vs. charge multiplicity of theproduced particles, we can make fits to produced particles, we can make fits to

search for hard processes (search for hard processes (>1.0).>1.0).

The results are:The results are:

To conclude this presentation I’ll move to To conclude this presentation I’ll move to an absolute intellectual speculation: a dreaman absolute intellectual speculation: a dreamby Richard Dawkins (The blind Watchmaker;by Richard Dawkins (The blind Watchmaker;Ed. Norton, 1996). A Ed. Norton, 1996). A taletale about about evolutionevolution!!

Let’s start from basic. a stick: duplicate, reduce,Let’s start from basic. a stick: duplicate, reduce,add. Repeat ……. n times; keep the proportion.add. Repeat ……. n times; keep the proportion.Let’s start from basic. a stick: duplicate, reduce,Let’s start from basic. a stick: duplicate, reduce,add. Repeat ……. n times; keep the proportion.add. Repeat ……. n times; keep the proportion.

Clearly you may choose: angle, different length inClearly you may choose: angle, different length inthe Y, different vert./horiz. scales and the likes.the Y, different vert./horiz. scales and the likes.Dawkins calls these “genes” able to influence theDawkins calls these “genes” able to influence the““evolutionevolution” of the “fractal structure”.” of the “fractal structure”.

Clearly you may choose: angle, different length inClearly you may choose: angle, different length inthe Y, different vert./horiz. scales and the likes.the Y, different vert./horiz. scales and the likes.Dawkins calls these “genes” able to influence theDawkins calls these “genes” able to influence the““evolutionevolution” of the “fractal structure”.” of the “fractal structure”.

Add a “gene” ableAdd a “gene” ableto force cutting to force cutting

the structure evolu-the structure evolu-tion after, say, 5tion after, say, 5steps. Assume asteps. Assume a

total of 10 “genes”total of 10 “genes”properly chosen.properly chosen.

Add a “gene” ableAdd a “gene” ableto force cutting to force cutting

the structure evolu-the structure evolu-tion after, say, 5tion after, say, 5steps. Assume asteps. Assume a

total of 10 “genes”total of 10 “genes”properly chosen.properly chosen.

Here are 9 genesHere are 9 genesHere are 9 genesHere are 9 genes

Now let a programNow let a programmake random choicemake random choice

of the gene to be of the gene to be used at every stepused at every step

and make 29 of them,and make 29 of them,not counting the 10not counting the 10thth

““stop” gene (Dawkinsstop” gene (Dawkinscalls “evolutions” the calls “evolutions” the steps…), according to steps…), according to a cumulative selectiona cumulative selectionstrategy: i.e to selectstrategy: i.e to selectwhat looks more simi-what looks more simi-lar to known objects.lar to known objects.

Now let a programNow let a programmake random choicemake random choice

of the gene to be of the gene to be used at every stepused at every step

and make 29 of them,and make 29 of them,not counting the 10not counting the 10thth

““stop” gene (Dawkinsstop” gene (Dawkinscalls “evolutions” the calls “evolutions” the steps…), according to steps…), according to a cumulative selectiona cumulative selectionstrategy: i.e to selectstrategy: i.e to selectwhat looks more simi-what looks more simi-lar to known objects.lar to known objects.

Here is one resultHere is one result

swallow tail clown lunar module Precision scale

insect larva scorpion cathouse woody frog

spitfire Crossed swords wasp Crustacean shellfish

insect fox lamp spider monky bat

SelectedSelected choice ofchoice ofresults results from 29from 29

step seriesstep series

substitutsubstitutee

sticks sticks withwith

cells; letcells; letthe the

seriesseriesgo for 11go for 11billion billion

years ….years ….Wait andWait andsee!!!!!see!!!!!