some works involving (multi)...
TRANSCRIPT
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Some works involving (multi) fractals
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There is a kind of self similarity attrributes (and sense learning) at different levels…
O Lineal?
O Not lineal?
O Self affinity (similarity)…
But…..is self affinity perceived by our senses
as homogeneous (or otherwise) along the
whole eating experience?
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FOR INSTANCE:
O Eating pasta……
We expect the whole duration of our italian
degustation experience will be as our
senses predicted…
The first bite, the second, the third, etc will
taste to pasta, YES…”degraded and more
degraded IN the mouth and latter in our
digestive system….AND NOT……
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I buy and eat pasta and…
O Second (or third, etc) bite has the texture of an apple…?!
or a nacho….?! this was obviously not expected….
THERE IS A VERY COMPLEX LEARNING PROCESS IN MANY ASPECTS OF FOOD CONSUPTION.
AND IN MANY WAYS AND WITH TIME, WE CAN PREDICT WHAT IS GOING TO BE LIKE THE NEXT EATING STAGE…
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MAY MASTICATION BE A PROCESS FOR GENERATING MULTIFRACTAL
SURFACES?
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
… watch and learn,
I’ll show you how
you can proceed
with multifractality
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MULTIFRACTALITY
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
O Different patterns (statistically different
scale dependence) merged to form one total
structure
log ε
Fractal dimension
log N
Self-affinity
(monofractal) No self-affinity
Self-affinity
(multifractal)
Different
dependence
behaviours
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MULTIFRACTALITY
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
O A multifractal structure can be considered
as a superposition of homogeneous
monofractal structures.
O Therefore there is not a unique value of DF
but a spectrum (distribution) of self-affinity
dimensions.
Chhabra et al., 1989
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MULTIFRACTAL ANALYSIS
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
O Probability distribution of pixels in ε-sized boxes
ε = 20 km
N = 139 Therefore:
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MULTIFRACTAL ANALYSIS
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
O
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MULTIFRACTAL ANALYSIS
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
O Spectrum D(q) vs q. Multifractal sets can also be characterized
through the scaling of the qth order moments of Pi,ε
distributions
Multifractal
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MULTIFRACTAL ANALYSIS
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
O The measurements of multifractals are mainly
the measurements of a statistical distribution,
which is why the results yield useful information
even if the underlying structure does not show a
self-affine behaviour.
O Thereby: multifractal analysis should be explored
as a first step in order to determine the
statistical behaviour of a pattern or figure.
Plotnick et al., 1996
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ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
Plotnick et al., 1996
Multifractal analysis- Applications
In the fields:
Astronomy and Cosmology
Atmospheric Science
Biology and Bioengineering
Chemical Reactions
Civil Engineering and Architecture
Electrical Engineering
Financial forecast
Food Science
Geology and Seismology
Histopathology
Informatics
Linguistics
Music
Pharmaceutical technology
Physics
Textile industry
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ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
OUR WORKS
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ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
STUDY OF BREAKAGE IN FOOD,
MODELLING BY IMAGE ANALYSIS AND NON-LINEAR DYNAMICS
Evangelina García Armenta
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1. Division or separation of an object in different parts after applying a force or stress on it
2. Maximum point of the stress-strain curve
van den Berg et al., 2008
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
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ε
σ
Askeland y Phulé, 2004.
Young´s modulus
E Elasticity
modulus
σ stress
ε strain
Elastic
deformation Microfracture
Breakage point
(catastrophic
failure)
Plastic
deformation
Permanent deformation
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
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ImageJ v.1.47
Parameters: fractal dimension, fracture’s length and lacunarity
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
Digital image analysis
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RESULTS
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
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RESULTS
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
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INFLUENCE OF MOISTURE CONTENT
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
0,5
0,7
0,9
1,1
1,3
1,5
0 1 2 3 4 5 6 7 8
Frac
tal d
ime
nsi
on
Moisture content(%)
1.01 -1.09
Breakage of fried corn chips (nachos)
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INFLUENCE OF MOISTURE CONTENT
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
Breakage of fried corn chips (nachos)
0
10
20
30
40
50
60
70
80
2 parts 3 parts 4 parts Perforation Crack No breakage
Pe
rce
nt
of
bro
ken
ch
ips
Type of breakage
1%
7%
Moisture content
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ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
IMAGE ANALYSIS AS A TOOL FOR
QUANTITATIVELY DESCRIBING THE
SENESCENCE PROCESS IN PRE-
CUT, FRESH PAPAYA (Carica papaya L.)
Gabriela Cáez
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ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
Initial 30 min
60 min 90 min
120 min 150 min
180 min 210 min
240 min 4°C 240 min 37°C
240 min 4°C 240 min 37°C
4 ºC
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ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
Papaya verde inicial tejido interno 10X Papaya Madura Tejido interno 10X
Papaya verde Tejido interno Expuesto 10X Papaya madura Tejido interno Expuesto 10X
Figura 5. Micrografías confocal. El color verde se asocia a los compuestos tipo carbohidrato de la lámina
media y el color rojo a pigmentos que fluorecen en el rango de la clorofila.
A B
C D
Internal tissue. 10 x Internal tissue. 10 x
Internal tissue. 10 x Internal tissue. 10 x
No
exp
osit
ion
E
xpo
sit
ion
at
20
ºC
an
d 6
0%
RH
Fresh Mature
Confocal
microscopy
Green
and red
emission
spectra
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ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
1,4
1,9
2,4
2 2,2 2,4 2,6
F (α
)
α
2
2,2
2,4
2,6
-20 0 20
D (
q)
Q
Fresh papaya
Before exposition After exposition G
ree
n e
mis
sio
n
Re
d e
mis
sio
n
1,4
1,9
2,4
1,8 2,3 2,8
F (α
)
α
2
2,2
2,4
2,6
-20 0 20
D (
q)
Q
0
1
2
0 2 4
F (α
)
α
0
2
4
-20 0 20
D (
q)
Q
1
2
3
1,5 2 2,5
F (α
)
α
1,8
2
2,2
-20 0 20
D (
q)
Q
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ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
Mature papaya
Before exposition After exposition G
ree
n e
mis
sio
n
Re
d e
mis
sio
n
0
2
4
1 2 3
F (α
)
α
1,8
2
2,2
2,4
-20 0 20
D (
q)
Q
0
2
4
1 2 3
F (α
)
α
0
2
4
-20 0 20
D (
q)
Q
0
2
4
1 2 3
F (α
)
α
1,8
2
2,2
-20 0 20
D (
q)
Q
0
2
4
0 2 4
F (α
)
α
0
2
4
-20 0 20
D (
q)
Q
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ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
OTHER WORKS RELATED WITH NON-LINEAR DYNAMICS
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Hydrodynamics of disintegration
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
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a
f (x, y) = [(1.1 + 0.91 (xi cos Q + yi sen Q)), (0.91 (-xi sen Q + yi cos Q))]
Q = (-5.6) / (1+xi2+yi
2)
b
c
e d
-20
-10
0
10
20
30
40
-20 -10 0 10 20 30 40 50 60
Position in "x" axis (pixel)
Po
sit
ion
in
"y"
axis
(p
ixel)
-30
-20
-10
0
10
20
30
-20 -10 0 10 20 30 40 50 60
Position in "x" axis (pixel)
Po
sit
ion
in
"y"
axis
(p
ixel)
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-1 -0.5 0 0.5 1 1.5 2
Position in "x" axis (mm)
Po
sit
ion
in
"y"
axis
(m
m)
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
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ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
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O Attempting to “enter” into the black box
Processes and Fundamentals
Phenomena
Tools Interpretation
Design, equipments and processes
Operating conditions Functionality
Shelf life
Packaging materials, etc.
Beyond the
structure
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials
BUILDING THE BRIDGE
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AND BRIDGING….
STRUCTURE
PROCESSING
FUNCTION
INTEGRATED APPROACH
BEYOND THE STRUCTURE
Consequences (and
implications)
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TEAM O Liliana Alamilla
O Gustavo Barbosa-Cánovas
O José Miguel Aguilera
O Ximena Quintanilla
O DaríoTétez
O Domingo Mery
O Jorge Welti
O Jorge Chanona
O Ebner Azuara
O Ignacio Beristain
O Georgina Calderón
O Reynold Farrera
O Humberto Hernández
O Antonio Jiménez
O Cristian Jiménez
O Cynthia Cano
O Amor Monroy
O Miriam Fabela
O Itzel García-Luna
O Josefina Porras
O Evangelina García Armenta
O Brenda Camacho
O Gabriela Cáez
O Fabiola Guzmán
O Verónica Freyre
O Andrea Lezama
O Rosalva Mora
O Alicia Ortiz
O Antonio Pérez-Nieto
O Jaime Vernon
O Enrique Flores
O Luz Alicia Pascual
O Carolina Gumeta
O Sofía Meraz
O Israel Arzate
O Rubí Viveros
O Raúl y Jaime
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THANK YOU!
ESPCA/São Paulo School of Advanced Science
Advances in Molecular Structuring of Food Materials