David G. Martin
PhD student in theoretical physics supervised by Julien Tailleur.
MSC complex systems lab, Paris Diderot.
Former student at ENS Paris.
Resume Research StatementResearch interests
I am mainly interested in statistical physics and its broad applications to biology, population dynamics or finance. My PhD subject tackle emerging collective properties in active matter but I have also worked on exploreexploit paradigms and on stochastic thermodynamic. Active Matter describes systems extracting energy from their environment at the microscopic scale, thus driving them far from equilibrium. Activity is encountered at all scales in nature, from molecular motor to flies swarm, passing through the canonical examples of swimming organisms (bacteria) or artificial swimmers (Janus colloids). The physics exhibited by such systems is very rich, often displaying a wealth of emerging collective properties and achieving complex cohesive states of matter. The main goal of my PhD is to theoretically elucidate how active particles reach such an intricated, largescale structure.

Effect of translational noise on Active Ornstein Uhlenbeck Particles
Usual brownian particles are only submitted to a gaussian white noise exhibiting no characteristic time. A more realistic model would further include additional fluctuations, endowed with such a memory time. Unfortunately, this colored noise drives the particle outofequilibrium and hinders analytical computations. I developed an exact perturbative expansion of the corresponding steadystate density, opening up theoretical insights for such a model. Together with Thibaut Arnoulx de Pirey, we used it to derive quantitative formulas for three activityinduced phenomena : the deviation from Boltzmann's distribution, the emergence of ratchet current, and the entropy production rate. Surprisingly, we found that these last two signatures, namely the current and the entropy production rate, can be nonmonotonic functions of T. Thus, depending on context, switching on translational diffusion may drive the particle closer to or further away from equilibrium.Publications :

Statistical Mechanics of Active Ornstein Uhlenbeck Particles
I developed in details the physic of Active Ornstein Uhlenbeck Particles (AOUPs), a canonical model of active agents. More particularly, I devised a perturbative scheme yielding the exact stationary measure at small activity. Building on this new result, I made quantitative predictions on activityinduced phenomena such as accumulation near walls and current emergence in Feymann ratchet. Such features of AOUPs had previously been observed and expected but had never been described both qualitatively and quantitatively. Careful langevin simulations using a Heun scheme coupled to an exact numerical integration of the active noise validated my formulas.Publications :

Emergence of collective motion in topologically aligning models
I studied the order of the transition to collective motion at the fieldtheoretical level. By using quasi linear renormalization, I showed that the fluctuations of the order parameter are triggering a densitydependent shift of the critical temperature. For metric model, this shift generically turns a spurious mean field continuous transition into a discontinuous one. Surprisingly, the mechanism also holds for topological models in which lengthfree interactions were previously believed to lead to continuous transitions. I confirmed my analytical predictions both by direct simulations of stochastic field theories (semi spectral method) and by numerical implementation of microscopic models (interacting langevin dynamic).Publications :

Activityinduced solidification
In experiments realized in the group of D. Bartolo, dense assemblies of Quincke rollers collectively propelling undergo an arrested phase separation above a critical density : they lose their orientational order and jam. Combining flocking equations with the slowing down of rollers upon increasing density (or the physic of MIPS), I developed a minimalist hydrodynamic theory to account for this phenomenology. Solving numerically my PDE by using a semispectral scheme, I indeed showed the existence of a first order phase transition between a jammed solid state and a polar liquid state.Publications :

Optimal growth for Parabolic Anderson Model endowed with colored noise
The dilemma between the collection of available goods, whose instantaneous rate fluctuate or get depleted, and the stochastic search for new resources lies at the core of the exploreexploit paradigm widely observed in nature : cell colonies spreading in an environment, bankers reinvesting profits...
Optimal mining strategies are slaved to two timescales; one set by the variability of the environment, and the other by the speed of the explorative process. Indeed, if a spot remains fertile during a finite duration neither staying on it for too long (and seeing it depleted) nor leaving it very rapidly (and failing to harvest it properly) will maximize growth. There is, however, an additional lurking danger that must be coped with : localization. One might end up with a distribution concentrated among few abundant patches, and thus in a risky position with respect to shocks.
It is interesting to remark that all these characteristic features are encompassed in simple stochastic growth models, whose analytical and numerical study lies within the reach of current physicist technics. These minimalists model can be further confronted with real data, being it econophysic data (bonds, share) or biological data (cell colonization, population spreading).
Publications :

Thermodynamic engine fuelled by active particles
Stochastic thermodynamic is a theoretical framework allowing microscopic definitions of thermodynamic quantities such as heat, work or energy. When averaged over the phasespace, these quantities can be mapped to their corresponnding macroscopic counterparts and one can show that they are consistents with the empirical laws of thermodynamic.A canonical experiment exploiting stochastic thermodynamic is the colloidal heat engine : a colloidal tracer is immersed into a fluctuating bath and confined by a potential. The external operator can then vary both the confining potential and the fluctuations of the bath to create a microscopic heat engine. During the past decade, several experimental realizations have demonstrated the feasibility of building such engines, both for an equilibrium and a nonequilibrium bath.
One might then wonder what happens when the tracer becomes active : is it still possible to correctly define microscopic thermodynamic quantities ? Do they still map to macroscopic ones ? Does activity enhance or reduce the engine's power production ?
Publications :
Teaching experiences
So far, I have mainly given lectures in the medicine cursus at Paris Descartes University.
 (20182020) Physics lectures in first year of medicine cursus (PACES) at Paris Descartes University : electrostatic, hydrodynamic, hydrostatic, perfect fluids.
 (20182020) Wave optics lectures in second year of pharmacy cursus at Paris Descartes University.
 (20182020) Optical geometry lab work sessions in second year of pharmacy at Paris Descartes University.
Publications
 D. G. Martin and T. Arnoulx de Pirey
AOUP in the presence of Brownian noise: a perturbative approach
J. Stat. Mech. 043205 (April 2021), arXiv 2009.13476
JSTAT arXiv  D. G. Martin, J. O'byrne, M. E. Cates, E. Fodor, C. Nardini, J. Tailleur and F. Van Wijland
Statistical Mechanics of Active Ornstein Uhlenbeck Particles
Phys. Rev. E 103, 032607 (March 2021), arXiv 2008.12972
PRE arXiv  D. G. Martin, H. Chaté, C. Nardini, A. Solon, J. Tailleur and F. Van Wijland
Fluctuationinduced phase separation in metric and topological models of collective motion
Phys. Rev. Lett. 126, 148001 (April 2021), arXiv 2008.01397
PRL arXiv  D. Geyer, David G. Martin, J. Tailleur and D. Bartolo
Freezing a Flock: MotilityInduced Phase Separation in Polar Active Liquids
Phys. Rev. X 9 031043, arXiv 1903.01134
PRX arXiv  Thomas Gueudré and David G. Martin
Optimal growth entails risky localization in population dynamics
EPL (Europhys. Lett.) 121, 68005 (may 2018) arXiv 1712.00979
Selected as editor's choice
Selected as EPL Highlights
EPL arXiv  D. Martin, C. Nardini, M. E. Cates, and É. Fodor
Extracting maximum power from active colloidal heat engines
EPL (Europhys. Lett.) 121, 60005 (may 2018) arXiv 1803.01620
Selected as editor's choice
Selected as EPL Highlights
EPL arXiv
Fellowships/Prizes/Awards
 20212024 : Kadanoff Postdoctoral Fellowship at the University of Chicago.
 20212022 : Joint travel grant FACCTS of 25k$ with Vincenzo Vitelli at the University of Chicago.
 September 2019 : best poster prize award at the frenchgerman WEHeraeus Seminar "Novel physics in living systems" in Roscoff, France.
Contact Me
Laboratoire MSC, Paris
10 rue Alice Domon et Léonie Duquet, 75205 Paris cedex 13, France
David.Martin@univparisdiderot.fr