IDO REGEV - THEORETICAL SOFT MATTER PHYSICS

Classical statistical mechanics and condensed matter physics

Nonlinear dynamics and chaos

Continuum mechanics

Tools

Topics

Physics of glasses and granular materials

Drying and cracking of soft and granular materials

Pattern formation and biomechanics in developmental biology

Various Numerical Methods

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AMORPHOUS MATERIALS UNDER PLASTIC DEFORMATION

Transition to chaos

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Figure 1. Linking transport and geometry. (a) Snapshot of a domain wall in atwo dimensional ferromagnet [27]. (b) Typical velocity-force characteristics. (c)Crossover lengths ℓopt and ℓav representing the optimal excitation and the deter-ministic avalanches, respectively. (d) Geometric crossover diagram.

sity waves and vortices, the elastic structure is periodic [17,18], while infracture [14,19,20,21,22] and wetting [23,24] the elastic interactions are longranged. Moreover, anharmonic corrections to the elasticity or anisotropies canbe also relevant [25,26]. Remarkably, all these different universality classes(with different critical exponents) share the same basic physics of the QEWmodel discussed in the following sections.

2 Transport and Geometry of Driven Interfaces in Random Media

Disorder makes the interface dynamics very rich. On one side, the interfaceappears rough, both in absence and in presence of drive. On the other side,the response of the system to a finite drive is strongly nonlinear and, at zerotemperature, motion exists only above a finite threshold, the so-called criticalforce fc. As summarized in Fig. 1 collective dynamics is observed in differentregimes: just above fc the motion is very jerky, and displays collective rear-rangements or avalanches of a typical size ℓav. Below fc motion is possible onlyby thermal activation over energy barriers and the interface slowly fluctuatesbackward and forward. This “futile” and reversible dynamics takes place up

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AMORPHOUS MATERIALS UNDER PLASTIC DEFORMATION

Non-equilibrium critical point

Avalanche dynamics

Nature Reviews | Genetics

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Posterior extension

Determinedsegments Tail budSomites

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Nucleus Cytoplasm

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Gene expression waves Mean-field coupling

12 somites 19 somites

5 20 35Somite number

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0

400

800

1,200

1,600

Tim

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200 m

180 min 300 min 540 min 780 min5 somites

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a Embryonic somitogenesis

b

d Spatially coordinated genetic oscillations

c Minimal cell autonomous oscillator model

Hes/Her protein

Period (T)Segmentlength (S)

REVIEWS

526 | AUGUST 2009 | VOLUME 10 www.nature.com/reviews/genetics

Elongation due to Cellular diffusion

Nature Reviews | Genetics

S = vT

S

Hes/her

AAAAA

AAAAATp

Tm

m

Posterior extension

Determinedsegments Tail budSomites

Notochord

Nucleus Cytoplasm

p A

PSM

Embryonic extension velocity (v)

Gene expression waves Mean-field coupling

12 somites 19 somites

5 20 35Somite number

–400

0

400

800

1,200

1,600

Tim

e (m

in)

200 m

180 min 300 min 540 min 780 min5 somites

Frequency profile(slowing oscillations)

Clock(generation and synchronizationof oscillations)

Tim

e (o

ne c

ycle

of c

lock

)

50 m

Wavefront(arrest of oscillation)

e Spatially extended clock and wavefront model

Hes/her mRNA

27 somites Period = 24.5 0.8 min(n = 9, T = 27.4 0.1 °C)

a Embryonic somitogenesis

b

d Spatially coordinated genetic oscillations

c Minimal cell autonomous oscillator model

Hes/Her protein

Period (T)Segmentlength (S)

REVIEWS

526 | AUGUST 2009 | VOLUME 10 www.nature.com/reviews/genetics

Nonlinear gene expression waves prescribe vertebra sizes

From gene expression to growth and form

DEVELOPMENTAL BIOLOGY

Lateral Plate

Wall friction

Wall friction

Neural Tube

Particle flux

Moving wall

Som

ite

Som

ite

Som

ite

Som

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PosteriorAnterior

DRYING AND CRACKING

Drying causes volume gradients

Volume gradients cause compatibility strains - causes fracture and peeling

Emerging length-scale (not from internal structure)

Strain compatibility