Article – Page 11 – Soft Matter Lab

Review on Multiplicative Noise published in Rep. Prog. Phys.

Effective drifts in dynamical systems with multiplicative noise: A review of recent progress (Invited review)
Giovanni Volpe & Jan Wehr
Reports on Progress in Physics 79(5), 053901 (2016)
DOI: 10.1088/0034-4885/79/5/053901
arXiv: 1511.05340

Noisy dynamical models are employed to describe a wide range of phenomena. Since exact modeling of these phenomena requires access to their microscopic dynamics, whose time scales are typically much shorter than the observable time scales, there is often need to resort to effective mathematical models such as stochastic differential equations (SDEs). In particular, here we consider effective SDEs describing the behavior of systems in the limits when natural time scales become very small. In the presence of multiplicative noise (i.e. noise whose intensity depends upon the system’s state), an additional drift term, called noise-induced drift or effective drift, appears. The nature of this noise-induced drift has been recently the subject of a growing number of theoretical and experimental
studies. Here, we provide an extensive review of the state of the art in this eld. After an introduction, we discuss a minimal model of how multiplicative noise affects the evolution of a system. Next, we consider several case studies with a focus on recent experiments: the Brownian motion of a microscopic particle in thermal equilibrium with a heat bath in the presence of a diffusion gradient; the limiting behavior of a system driven by a colored noise modulated by a multiplicative feedback; and the behavior of an autonomous agent subject to sensorial delay in a noisy environment. This allows us to present the experimental results, as well as mathematical methods and numerical techniques, that can be employed to study a wide range of systems. At the end we give an application-oriented overview of future projects involving noise-induced drifts, including both theory and experiment.

Microscopic Crowd Control published in Nature Commun.

Disorder-mediated crowd control in an active matter system
Erçağ Pinçe, Sabareesh K. P. Velu, Agnese Callegari, Parviz Elahi, Sylvain Gigan, Giovanni Volpe & Giorgio Volpe
Nature Communications 7, 10907 (2016)
DOI: 10.1038/ncomms10907

Living active matter systems such as bacterial colonies, schools of fish and human crowds, display a wealth of emerging collective and dynamic behaviours as a result of far-from- equilibrium interactions. The dynamics of these systems are better understood and controlled considering their interaction with the environment, which for realistic systems is often highly heterogeneous and disordered. Here, we demonstrate that the presence of spatial disorder can alter the long-term dynamics in a colloidal active matter system, making it switch between gathering and dispersal of individuals. At equilibrium, colloidal particles always gather at the bottom of any attractive potential; however, under non-equilibrium driving forces in a bacterial bath, the colloids disperse if disorder is added to the potential. The depth of the local roughness in the environment regulates the transition between gathering and dispersal of individuals in the active matter system, thus inspiring novel routes for controlling emerging behaviours far from equilibrium.

Featured in:
“Understanding the dynamics of crowd behavior”, Phys.com
“Understanding the dynamics of crowd behavior”, ScienceDaily.com
“Physics Explains Group Dynamics: When There’s Chaos, Individuals Disperse”, Medical Daily
“Ученые выяснили, как меняющаяся окружающая среда влияет на движение толпы”, Gazeta.ru
“Understanding the dynamics of crowd behaviour”, Nano
“Understanding the dynamics of crowd behaviour”, Noodls
“Understanding the dynamics of crowd behavior”, EurekAlert!
“Understanding the dynamics of crowd behavior”, Informs
“Understanding the dynamics of crowd behavior”, Nanowerk

The Small-mass Limit for Langevin Dynamics published in J. Stat. Phys.

The small-mass limit for Langevin dynamics with unbounded coefficients and positive friction
David P. Herzog, Scott Hottovy & Giovanni Volpe
Journal of Statistical Physics 163(3), 659—673 (2016)
DOI: 10.1007/s10955-016-1498-8
arXiv: 1510.04187

A class of Langevin stochastic differential equations is shown to converge in the small-mass limit under very weak assumptions on the coefficients defining the equation. The convergence result is applied to three physically realizable examples where the coefficients defining the Langevin equation for these examples grow unboundedly either at a boundary, such as a wall, and/or at the point at infinity. This unboundedness violates the assumptions of previous limit theorems in the literature. The main result of this paper proves convergence for such examples.

Engineering of Sensorial Delay published in Phys. Rev. X

Engineering sensorial delay to control phototaxis and emergent collective behaviors
Mite Mijalkov, Austin McDaniel, Jan Wehr & Giovanni Volpe
Physical Review X 6(1), 011008 (2016)
DOI: 10.1103/PhysRevX.6.011008
arXiv: 1511.04528

Collective motions emerging from the interaction of autonomous mobile individuals play a key role in many phenomena, from the growth of bacterial colonies to the coordination of robotic swarms. For these collective behaviors to take hold, the individuals must be able to emit, sense, and react to signals. When dealing with simple organisms and robots, these signals are necessarily very elementary; e.g., a cell might signal its presence by releasing chemicals and a robot by shining light. An additional challenge arises because the motion of the individuals is often noisy; e.g., the orientation of cells can be altered by Brownian motion and that of robots by an uneven terrain. Therefore, the emphasis is on achieving complex and tunable behaviors from simple autonomous agents communicating with each other in robust ways. Here, we show that the delay between sensing and reacting to a signal can determine the individual and collective long-term behavior of autonomous agents whose motion is intrinsically noisy. We experimentally demonstrate that the collective behavior of a group of phototactic robots capable of emitting a radially decaying light field can be tuned from segregation to aggregation and clustering by controlling the delay with which they change their propulsion speed in response to the light intensity they measure. We track this transition to the underlying dynamics of this system, in particular, to the ratio between the robots’ sensorial delay time and the characteristic time of the robots’ random reorientation. Supported by numerics, we discuss how the same mechanism can be applied to control active agents, e.g., airborne drones, moving in a three-dimensional space. Given the simplicity of this mechanism, the engineering of sensorial delay provides a potentially powerful tool to engineer and dynamically tune the behavior of large ensembles of autonomous mobile agents; furthermore, this mechanism might already be at work within living organisms such as chemotactic cells.

Featured in “Focus: Sensing Delays Control Robot Swarming”, Physics 9, 13 (January 29, 2016)

POLICRYPS to Generate Cylindrical Vector Beams published in Appl. Phys. Lett.

Polar POLICRYPS diffractive structures generate cylindrical vector beams
Domenico Alj, Sathyanarayana Paladugu, Giovanni Volpe, Roberto Caputo & Cesare Umeton
Applied Physics Letter 107(20), 201101 (2015)
DOI: 10.1063/1.4935605
arXiv: 1509.07671

Local shaping of the polarization state of a light beam is appealing for a number of applications. This can be achieved by employing devices containing birefringent materials. In this article, we present one such enables converting a uniformly circularly polarized beam into a cylindrical vector beam (CVB). This device has been fabricated by exploiting the POLICRYPS (POlymer-LIquid CRYstals-Polymer-Slices) photocuring technique. It is a liquid-crystal-based optical diffraction grating featuring polar symmetry of the director alignment. We have characterized the resulting CVB profile and polarization for the cases of left and right circularly polarized incoming beams.

Optical Control of Nanowire by Nanoaperture published in Opt. Lett.

Optical trapping and control of a dielectric nanowire by a nanoaperture
Mehdi Shafiei Aporvari, Fardin Kheirandish & Giovanni Volpe
Optics Letters 40(20), 4807—4810 (2015)
DOI: 10.1364/OL.40.004807
arXiv: 1507.04044

We demonstrate that a single sub-wavelength nanoaperture in a metallic thin film can be used to achieve dynamic optical trapping and control of a single dielectric nanowire. A nanoaperture can trap a nanowire, control its orientation when illuminated by a linearly polarized incident field, and rotate the nanowire when illuminated by a circularly polarized incident field. Compared to other designs, this approach has the advantage of a low-power driving field entailing low heating and photodamage.

Aberrant Cerebral Topology in Early Parkinson published in Human Brain Mapp.

Aberrant cerebral network topology and mild cognitive impairment in early Parkinson’s disease
Joana B. Pereira, Dag Aarsland, Cedric E. Ginestet, Alexander V. Lebedev, Lars-Olof Wahlund, Andrew Simmons, Giovanni Volpe & Eric Westman
Human Brain Mapping 36(8), 2980—2995 (2015)
DOI: 10.1002/hbm.22822

The aim of this study was to assess whether mild cognitive impairment (MCI) is associated with disruption in large-scale structural networks in newly diagnosed, drug-na€ıve patients with Parkin- son’s disease (PD). Graph theoretical analyses were applied to 3T MRI data from 123 PD patients and 56 controls from the Parkinson’s progression markers initiative (PPMI). Thirty-three patients were classified as having Parkinson’s disease with mild cognitive impairment (PD-MCI) using the Movement Disorders Society Task Force criteria, while the remaining 90 PD patients were classified as cognitively normal (PD- CN). Global measures (clustering coefficient, characteristic path length, global efficiency, small-world- ness) and regional measures (regional clustering coefficient, regional efficiency, hubs) were assessed in the structural networks that were constructed based on cortical thickness and subcortical volume data. PD-MCI patients showed a marked reduction in the average correlation strength between cortical and subcortical regions compared with controls. These patients had a larger characteristic path length and reduced global efficiency in addition to a lower regional efficiency in frontal and parietal regions com- pared with PD-CN patients and controls. A reorganization of the highly connected regions in the network was observed in both groups of patients. This study shows that the earliest stages of cognitive decline in PD are associated with a disruption in the large-scale coordination of the brain network and with a decrease of the efficiency of parallel information processing. These changes are likely to signal further cognitive decline and provide support to the role of aberrant network topology in cognitive impairment in patients with early PD.

Influence of Active Particles on Colloidal Clusters published in Soft Matter

Formation, compression and surface melting of colloidal clusters by active particles
Felix Kümmel, Parmida Shabestari, Celia Lozano, Giovanni Volpe & Clemens Bechinger
Soft Matter 11(31), 6187—6191 (2015)
DOI: 10.1039/C5SM00827A

We demonstrate with experiments and numerical simulations that the structure and dynamics of a suspension of passive particles is strongly altered by adding a very small (o1%) number of active particles. With increasing passive particle density, we observe first the formation of dynamic clusters comprised of passive particles being surrounded by active particles, then the merging and compression of these clusters, and eventually the local melting of crystalline regions by enclosed active particles.

Smoluchowski-Kramers Limit of SDE published in Commun. Math. Phys.

The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction
Scott Hottovy, Austin McDaniel, Giovanni Volpe & Jan Wehr
Communications in Mathematical Physics 336(3), 1259—1283 (2015)
DOI: 10.1007/s00220-014-2233-4
arXiv: 1404.2330

We study a class of systems of stochastic differential equations describing diffusive phenomena. The Smoluchowski-Kramers approximation is used to describe their dynamics in the small mass limit. Our systems have arbitrary state-dependent friction and noise coefficients. We identify the limiting equation and, in particular, the additional drift term that appears in the limit is expressed in terms of the solution to a Lyapunov matrix equation. The proof uses a theory of convergence of stochastic integrals developed by Kurtz and Protter. The result is sufficiently general to include systems driven by both white and Ornstein–Uhlenbeck colored noises. We discuss applications of the main theorem to several physical phenomena, including the experimental study of Brownian motion in a diffusion gradient.

Guide to Building Optical Tweezers published in JOSA B

A step-by-step guide to the realisation of advanced optical tweezers
Giuseppe Pesce, Giorgio Volpe, Onofrio M. Maragò, Philip H. Jones, Sylvain Gigan, Antonio Sasso & Giovanni Volpe
Journal of the Optical Society of America B 32(5), B84—B98 (2015)
DOI: 10.1364/JOSAB.32.000B84
arXiv: 1501.07894

Since the pioneering work of Arthur Ashkin, optical tweezers (OT) have become an indispensable tool for contactless manipulation of micro- and nanoparticles. Nowadays OT are employed in a myriad of applications demonstrating their importance. While the basic principle of OT is the use of a strongly focused laser beam to trap and manipulate particles, more complex experimental setups are required to perform novel and challenging experiments. With this article, we provide a detailed step-by-step guide for the construction of advanced optical manipulation systems. First, we explain how to build a single-beam OT on a homemade micro- scope and how to calibrate it. Improving on this design, we realize a holographic OT, which can manipulate independently multiple particles and generate more sophisticated wavefronts such as Laguerre–Gaussian beams. Finally, we explain how to implement a speckle OT, which permits one to employ random speckle light fields for deterministic optical manipulation.