Open Discussion on Self-Propelled Particle Models: Friday, May 9

Participants (alphabetic order):
Max Bi, Michael Hagan, Ananyo Maitra, Cristina Marchetti, Pawel Romanczuk, Saha Suropriya, Pragya Srivastava, Christoph Weber, Xingbo Yang

Scribe: Pawel Romanczuk (Please feel free to comment, add new aspects)

Main question: What are the different types of self-propelled particle models (SPP-models) ? Where do differences in the microscopic models play a role? What is universal? Note: We restrict ourselves here to the discussion of SPP-models with local interactions in space and time (e.g. no pure topological interactions).

There are many possibilities to classify microscopic models based on e.g.:

model formulation: discrete time and/or space (e.g. cellular automata) versus continuous time and space (stoch. differential equations)

the symmetries of the propulsion mechanism and the microscopic interactions (polar-polar, nematic-nematic, mixed)

the symmetries of the emergent ordered state(s)

Models with different microscopic dynamics may yield the same large-scale behavior (eg. orientationally ordered, fluid-like phase), which has universal properties independent on the microscopic model

The choice of the model depends on the scientific question of interest: e.g large-scale properties of a particular phase, versus (detailed) modelling of a particular experimental system. So first you need to ask the question "What do I want to model and why?".

Based on the symmetries of the "desired" large-scale behavior, one can cook-up a simple microscopic models which are likely to produce it (e.g. polar orientational order -> Vicsek-like model),

The other way round it is much more difficult: In general, it is not easy to predict the emergent phases from some non-trivial interaction rules, and for example interaction rules without explicit alignment may eventually lead also to emergence of long-ranged polar order via more subtle effects.

If you are interested only in the large-scale behavior of the system (a particual "phase" in a "thermodynamic" sense), a lot of models in the literature are equivalent, so one can go with a simple one (but you have to be aware that your transport coefficients in the hydrodynamic equations may have different dependencies on density)

If you are interested in the emergence of a particular state, transient dynamics and finite systems etc. the behaviour of different microscopic models, equivalent in the above sense, may be very different

Detailed binary collisions studies for various interactions used in SPP-models yield often very inconclusive results, e.g. depending on the collision angle and parameter they may be lead to polar alignment, nematic alignment or have no effect (rel. angle in = rel. angle out) -> Multi-particle effects strongly matter (emergence of local order as a true collective effect)

Does inertia play a role for the emergent phases? In general, if the relevant time scale of relaxation is much shorter than any time-scales of interest, then it should not matter. However, if one has active particles with an additional degree of freedom with a finite relaxation time (in principle also possible in an active, overdamped system -> "quasi-inertia"), this effects may become important; Possible impact? will depend on the model: either "only" shifting of critical lines, or new instabilities possible.

...

Discussion Session on Synchronization phenomena in active matter : Friday, April 25

Scribe: Xingbo Yang - Feel free to edit and comment

In the modeling of active matter, each unit is traditionally treated as static force multipoles, such as force dipole for pusher or puller of swimmers.
However, many active units, including swimmers, have an internal dynamic cycle which can be described by a phase variable. This internal degree of freedom
can be important in regulating the interactions and ultimately leads to novel collective behaviors of the active system, of which synchronization is a
prominent phenomenon (Leoni and Liverpool PRE 2012, PRL 2014, Furthauer and Ramaswamy PRL 2013).

Some of the challenging questions on this new topic are:

1. Is static active matter phase coherent or incoherent?

2. Does it make sense to think about the synchronization of dry (Toner-Tu) models?

3. Is the timescale for vorticity diffusion important when phase dynamics is considered?

4. How does synchronization affects the dynamics of polar/nematic order?

Group Discussion on Role of Quenched Disorder in Active Systems : Thursday, March 27

led by John Toner

Scribe: Pragya Srivastava - Please feel free to edit and comment.

Recent work has started to investigate the role of quenched (as opposed to annealed) disorder (QD) in active systems. One model considered recently by Toner and Guttenberg (see Toner’s seminar on March 17) is obtained by replacing noise in the Vicsek model by a finite concentration of `dead birds’ described as vectors with a fixed random direction. Live birds interact via the Vicsek alignment rule with both live and dead birds, but dead birds are fixed in space. The strength of disorder is controlled by assigning a weight to the interaction of live birds with dead ones. A continuum realization of the model is obtained by adding a spatially varying, but time-independent random force to the velocity equation in the Toner-Tu model. The random force has short-ranged correlations of strength ∆Q.
Some of the questions that were discussed include:

1. What is the role of such vector QD on a polar ordered flock? Toner argued that flocking is robust against QD (as well as against annealed disorder) and the flock has LRO and QLRO in d=3 and d=2, respectively. This is in contrast to the passive counterparts where QD destroys LRO and QLRO in d=3 and d=2, respectively.

2. What is the relation of this model to the one with extended randomly placed scattering sites studied recently by Peruani’s group? (see Peruani’s talk on Feb. 5 talk ).
It seems that in spite of the different language both models consider vectorial quenched disorder that tends to align the active units.
3. To a polar flock moving through QD, static QD should appear as a time dependent noise. What then makes QD different from `annealed' disorder?
A key point of difference is in the behavior of the sound modes of the polar flock which is clearly visible when the sound speed
vanishes at some `magic' angles (angle between the wave vector of perturbation and the direction of moving flock) due to the competition between convection and propagation. At these `magic' angles the fluctuations have large amplitudes.

4. What would be the effect of QD on active nematic? Is the hydrodynamic or generic instability suppressed or enhanced?
Competition between length scales: QD controls the correlation length of the nematic order parameter. This competes with the familiar length scale controlling the hydrodynamic instability proportional to √(K/α) with K the Frank constant and α the activity.

5. What about other way of incorporating QD? A random pressure would probably be less important.

6. Can the effect of QD be cast in terms of a inhomogeneous viscosity (if v is viewed as a velocity) or stiffness (if v is viewed as a polarization field)?

7. Not just an issue of theoretical interest. Quenched disorder could be important for bacteria swimming through porous media.

Discussion session, 31 Jan 2014

(Bullet point summary. Please expand and clarify as you see fit)

1. Modelling metastasis of cancer : Discussion on how did Paul Newton's group statistically their transition matrix by using the autopsy data set of untreated cancer patients. A monte-carlo like approach with a first guess involving choosing the row associated with a given primary cancer to be the eigenvector at the steady state. The transfer probabilities are unique to different types of primary tumor sites. The main difficulties in generalizing the transfer probabilities are: the lack of good temporal data, the small data set size, and interactions with treatment and patient-specific properties.

2. Long range order in 2d active systems : Toner and Tu, How general is this feature? Does it hold up when we go to high densities and start seeing dynamical features that are strange? Is it a better question to ask whether activity enhances or suppresses ordering rather than worry about the nature of said ordering?

3. What is activity? One good way to think about it might be to look at the scale of correlations in the driving and establish that this indeed happens at the microscale compared to the scale of observed emergent behavior

4. What different kinds of active matter systems are there? There is a huge number of microscopic model, but can we classify the long-scale, long-time macroscopic behavior of these systems using a small set of "classes"?
Possible classifications: i) Active particles can be polar (we distinguish head and tail) or apolar (when there is no head and tail and they do not exhibit "persistent" motion, ii) By symmetry of the particle-particle interactions: isotropic, polar, nematic. ii) By medium properties : momentum conserving or momentum sink.
Questions : How important are the details of the microscopic interactions/assumptions. For example, if we stayed within the momentum sink class above, how different would things be if we treated the velocity as underdamped instead of overdamped?

Discussion session, 10 Jan 2014

Scribe: Aparna Baskaran. Please feel free to edit and comment.

Initial conversation: Follow up from the previous discussion on what is active matter. For the moment let us suppose that internally driven materials is a definition.

One possible framework : Fix particular states of matter - elastic solid, viscous fluid, viscoelastic system, liquid crystals, colloids, glasses, composites.
The questions we ask in the context of conventional systems would be:
a) Mechanical response
b) Collective/Emergent behavior
c) defect dynamics in ordered phases
d) Pattern formation
etc
Now we ask the same questions in the context of the corresponding active state of matter.

Another framework (topic for a future discussion session): Start with a given system, namely a cell. List the key aspects of emergent behavior we would like to understand. Example: Motility, division, stress propogation,etc. Then discuss how we would go about addressing each of these features of this system. Then move up in scale to a collection of cells and formulate the key aspects at this level. (Moumita and Paul should annotate/expand this further, as I am trying to write their words as I heard them).

Introductory Meeting, 6 Jan 2014

Images from chalkboard

Organizational meeting of the focused working group on self-propellers. 3 Mar 2014.

(scribe: Mykola Tasinkevych)

Challenges and open question were discussed and are separated into two groups and itemized below.

1-body level:

Mechanisms of motions: self-phoretic, via shape variation in a bulk or by crawling on a substrate.

For the case of the shape-varying swimmers what is the role of the hydrodynamic interactions. For example what is relation between the flagellum polymorphism and tumbling events (rapid changes of the direction of the motion).

Another important issue is how to better control the directionality of self-propulsion without invoking external fields.

For the case of self-phoretic swimmers the scaling down the size of a swimmer.

Many-body level:

The main challenge here is how to pass from a swimming mechanism on the individual level to collective behavior of many active particles.

Construction of a continuum coarse-grained description.

How to incorporate effectively the hydrodynamic interactions and analyze their effects on resulting morphological phase transformations.

Motion of self-diffusiophoretic swimmers in oscillating chemical reactions and pattern formation in an underlying chemically patterned environment.

Discussion session, 20 Mar 2014. The closing session of the focused working group on self-propellers:

(scribe: Mykola Tasinkevych)

Experiments:

Currently experimental efforts are rather at a qualitative level, e.g., mere reporting on observation of various patterns formed by
self-propelled objects Therefore, from an experimental viewpoint there is a need for more quantitative and systematic experiment,
both on the one-body level (better characterization of the single particle motion) , as well as on the collective level.

Theory:

From the theoretical viewpoint the situation is also not satisfactory. Presently mostly numerical simulations are used, therefore
there is a big need for more basic analytical description of the collective phenomena, e.g. continuum coarse-grained models
similar to the active nematic, or active gel models . It is also challenging to correctly account for various effective interactions
among self-propellers. Moreover, non-equilibrium nature of the underlying processes make things very complicated: no unique
approach is at hands, all sort of details matters, etc. One the main question to be addressed by the future theory is the existence
of non-equilibrium critical universality classes?

Applications:

From the viewpoint of practical application there are many opened questions too.For example, could self-propellers be used
as micro-pumps. The clear vision of what are synthetic self-propellers good is still lacking.

I summary, the discussion showed the existence of several gaps to be bridged in the triangle theory-experiment-application.

Participants (alphabetic order):Open Discussion on Self-Propelled Particle Models: Friday, May 9Max Bi, Michael Hagan, Ananyo Maitra, Cristina Marchetti, Pawel Romanczuk, Saha Suropriya, Pragya Srivastava, Christoph Weber, Xingbo Yang

Scribe: Pawel Romanczuk (Please feel free to comment, add new aspects)

Main question: What are the different types of self-propelled particle models (SPP-models) ? Where do differences in the microscopic models play a role? What is universal?

Note: We restrict ourselves here to the discussion of SPP-models with local interactions in space and time (e.g. no pure topological interactions).

Discussion Session on Synchronization phenomena in active matter : Friday, April 25## Table of Contents

Scribe: Xingbo Yang - Feel free to edit and comment

In the modeling of active matter, each unit is traditionally treated as static force multipoles, such as force dipole for pusher or puller of swimmers.

However, many active units, including swimmers, have an internal dynamic cycle which can be described by a phase variable. This internal degree of freedom

can be important in regulating the interactions and ultimately leads to novel collective behaviors of the active system, of which synchronization is a

prominent phenomenon (Leoni and Liverpool PRE 2012, PRL 2014, Furthauer and Ramaswamy PRL 2013).

Some of the challenging questions on this new topic are:

1. Is static active matter phase coherent or incoherent?

2. Does it make sense to think about the synchronization of dry (Toner-Tu) models?

3. Is the timescale for vorticity diffusion important when phase dynamics is considered?

4. How does synchronization affects the dynamics of polar/nematic order?

Group Discussion on Role of Quenched Disorder in Active Systems : Thursday, March 27## led by John Toner

## Scribe: Pragya Srivastava - Please feel free to edit and comment.

Recent work has started to investigate the role of quenched (as opposed to annealed) disorder (QD) in active systems.One model considered recently by Toner and Guttenberg (see Toner’s seminar on March 17) is obtained by replacing noise

in the Vicsek model by a finite concentration of `dead birds’ described as vectors with a fixed random direction. Live birds interact

via the Vicsek alignment rule with both live and dead birds, but dead birds are fixed in space. The strength of disorder is controlled

by assigning a weight to the interaction of live birds with dead ones. A continuum realization of the model is obtained by

adding a spatially varying, but time-independent random force to the velocity equation in the Toner-Tu model. The random force has

short-ranged correlations of strength ∆Q.

Some of the questions that were discussed include:

1. What is the role of such vector QD on a polar ordered flock?

Toner argued that flocking is robust against QD (as well as against annealed disorder) and

the flock has LRO and QLRO in d=3 and d=2, respectively. This is in contrast to the passive

counterparts where QD destroys LRO and QLRO in d=3 and d=2, respectively.

2. What is the relation of this model to the one with extended randomly placed scattering sites studied recently by Peruani’s group?

(see Peruani’s talk on Feb. 5 talk ).

It seems that in spite of the different language both models consider vectorial quenched disorder that tends to align the active units.

3. To a polar flock moving through QD, static QD should appear as a time dependent noise. What then makes QD different from `annealed' disorder?

A key point of difference is in the behavior of the sound modes of the polar flock which is clearly visible when the sound speed

vanishes at some `magic' angles (angle between the wave vector of perturbation and the direction of moving flock) due to the competition between convection and propagation. At these `magic' angles the fluctuations have large amplitudes.

4. What would be the effect of QD on active nematic? Is the hydrodynamic or generic instability suppressed or enhanced?

Competition between length scales: QD controls the correlation length of the nematic order parameter. This competes with the familiar length scale controlling the hydrodynamic instability proportional to √(K/α) with K the Frank constant and α the activity.

5. What about other way of incorporating QD? A random pressure would probably be less important.

6. Can the effect of QD be cast in terms of a inhomogeneous viscosity (if v is viewed as a velocity) or stiffness (if v is viewed as a polarization field)?

7. Not just an issue of theoretical interest. Quenched disorder could be important for bacteria swimming through porous media.

## Discussion session, 31 Jan 2014

(Bullet point summary. Please expand and clarify as you see fit)1. Modelling metastasis of cancer : Discussion on how did Paul Newton's group statistically their transition matrix by using the autopsy data set of untreated cancer patients. A monte-carlo like approach with a first guess involving choosing the row associated with a given primary cancer to be the eigenvector at the steady state. The transfer probabilities are unique to different types of primary tumor sites. The main difficulties in generalizing the transfer probabilities are: the lack of good temporal data, the small data set size, and interactions with treatment and patient-specific properties.

2. Long range order in 2d active systems : Toner and Tu, How general is this feature? Does it hold up when we go to high densities and start seeing dynamical features that are strange? Is it a better question to ask whether activity enhances or suppresses ordering rather than worry about the nature of said ordering?

3. What is activity? One good way to think about it might be to look at the scale of correlations in the driving and establish that this indeed happens at the microscale compared to the scale of observed emergent behavior

4. What different kinds of active matter systems are there? There is a huge number of microscopic model, but can we classify the long-scale, long-time macroscopic behavior of these systems using a small set of "classes"?

Possible classifications: i) Active particles can be polar (we distinguish head and tail) or apolar (when there is no head and tail and they do not exhibit "persistent" motion, ii) By symmetry of the particle-particle interactions: isotropic, polar, nematic. ii) By medium properties : momentum conserving or momentum sink.

Questions : How important are the details of the microscopic interactions/assumptions. For example, if we stayed within the momentum sink class above, how different would things be if we treated the velocity as underdamped instead of overdamped?

## Discussion session, 10 Jan 2014

Scribe: Aparna Baskaran. Please feel free to edit and comment.Initial conversation: Follow up from the previous discussion on what is active matter. For the moment let us suppose that internally driven materials is a definition.

One possible framework : Fix particular states of matter - elastic solid, viscous fluid, viscoelastic system, liquid crystals, colloids, glasses, composites.

The questions we ask in the context of conventional systems would be:

a) Mechanical response

b) Collective/Emergent behavior

c) defect dynamics in ordered phases

d) Pattern formation

etc

Now we ask the same questions in the context of the corresponding active state of matter.

Another framework (topic for a future discussion session): Start with a given system, namely a cell. List the key aspects of emergent behavior we would like to understand. Example: Motility, division, stress propogation,etc. Then discuss how we would go about addressing each of these features of this system. Then move up in scale to a collection of cells and formulate the key aspects at this level. (Moumita and Paul should annotate/expand this further, as I am trying to write their words as I heard them).

## Introductory Meeting, 6 Jan 2014

Images from chalkboard

(scribe: Mykola Tasinkevych)Organizational meeting of the focused working group on self-propellers. 3 Mar 2014.Challenges and open question were discussed and are separated into two groups and itemized below.

1-body level:Many-body level:## Discussion session, 20 Mar 2014. The closing session of the focused working group on self-propellers:

(scribe: Mykola Tasinkevych)Experiments:Currently experimental efforts are rather at a qualitative level, e.g., mere reporting on observation of various patterns formed by

self-propelled objects Therefore, from an experimental viewpoint there is a need for more quantitative and systematic experiment,

both on the one-body level (better characterization of the single particle motion) , as well as on the collective level.

Theory:From the theoretical viewpoint the situation is also not satisfactory. Presently mostly numerical simulations are used, therefore

there is a big need for more basic analytical description of the collective phenomena, e.g. continuum coarse-grained models

similar to the active nematic, or active gel models . It is also challenging to correctly account for various effective interactions

among self-propellers. Moreover, non-equilibrium nature of the underlying processes make things very complicated: no unique

approach is at hands, all sort of details matters, etc. One the main question to be addressed by the future theory is the existence

of non-equilibrium critical universality classes?

Applications:From the viewpoint of practical application there are many opened questions too.For example, could self-propellers be used

as micro-pumps. The clear vision of what are synthetic self-propellers good is still lacking.

I summary, the discussion showed the existence of several gaps to be bridged in the triangle theory-experiment-application.