Complex systems

Usual Time: 

Upcoming Lectures

Nir Schreiber
24/01/2018 - 10:30
The Potts model has been widely explored in the literature for the last few decades. While many analytical and numerical results concern with the traditional two site interaction model in various geometries and dimensions, little is yet known about models where more than two spins simultaneously interact. We consider a ferromagnetic four site interaction Potts model on the Square lattice, where the four spins reside in the corners of an elementary square. Each spin can take an integer value $1,2,...,q$. We write the partition function as a sum over clusters consisting of monochromatic faces. When the number of faces becomes large, tracing out spin configurations is equivalent to enumerating large scale lattice animals. This, together with the observation that typically, in large animals, the number of sites (to leading order) is equal to the number of faces,implies that systems with $q\leq 4$ and $q>4$ exhibit a second and first order phase transitions, respectively.However, higher order terms can make the borderline $q=4$ systems fall into the first order regime.We find ${1}/{\log q}$ to be an upper bound on $T_c$, the exact critical point.Using a low temperature expansion, we show that ${1}/{\theta\log q}$, where $\theta>1$ is a $q$ dependent geometrical term, is an improved upper bound on $T_c$.Moreover, since large animals uniquely control long range order, we expect that $T_c=1/\theta\log q$.This expression is used to estimate the finite correlation length in the first order transition case.These results can be extended to other lattices.Our analytical predictions are confirmed numerically by an extensive studyof the four site interaction model using the Wang-Landau entropic sampling method for $q=3,4,5$.In particular, the $q=4$ model shows an ambiguous finite size pseudo-critical behavior.


Guy Bunin
07/03/2018 - 10:30


Previous Lectures

Yaakov Yudkin
17/01/2018 - 10:30

Different laser cooling mechanisms have been rising important questions from thermodynamics and statistical physics point of view ever since the beginning of this research field (over 40 years ago). Sisyphus cooling is especially well known in this respect providing experimentally accessible regime to study deviations from thermal equilibrium. Here we discuss the Doppler cooling mechanism (the most basic laser cooling mechanism which works even for a simple two-level atom) and show that it also supports deviations from Gaussian statistics for a certain parameters range. We study experimentally the Doppler cooling in Lithium and point out an interesting deviation from the simple, two-level theory, namely cooling at resonance. We develop a realistic theory which accounts for all energy levels of lithium atoms and all laser fields and show its successes and failures. 

Michael Assaf
27/12/2017 - 10:30

In the usual setting non-demographic noise, emanating, e.g., from environmental variability, is manifested by time-varying reaction rates. In this work we investigate a different type of non-demographic noise in the form of uncertainty in the reaction step-size, and demonstrate that this type of noise can have a dramatic effect on the stability of self-regulating populations. By employing the usual reaction scheme mA->kA, but allowing, e.g., the product number k to be a-priori unknown and sampled from a given distribution, we show that such non-demographic noise can greatly increase the population's stability compared to the case of fixed k. Our analysis is tested against numerical simulations, and by using empirical data of different species, we argue that certain distributions may be more evolutionary beneficial than others.

Moshe Schwartz
22/11/2017 - 10:30

 A number of complex physical systems will be presented in a unified way and the main idea of the SCE of mimicking the complex system by a simple but arbitrary simple system will be outlined. Two very simple problems will be presented as models for the application of the SCE, showing its obvious superiority over conventional treatments. Results for some of the complex systems including KPZ and noise driven Navier-Stokes will be discussed.

Yoav Pollack
15/11/2017 - 10:30 - 12:00

Inter-particle forces in amorphous solids such as glasses, colloids and granular material can be used to study phenomena such as jamming and force-chains. So far, no generally applicable methods exist for measuring the forces between each and every particle in the system. Our recently developed methods aim to x this unfortunate situation in both a-thermal and thermal systems, and produce some interesting insights as to the nature of these forces. In the a-thermal case all that is required for nding the force-law are the xed particle positions and the pressure. The method is shown to accurately recover the force-law in simulation. In the thermal case, we are developing a method to extract an eective potential, using the mean positions. This will allow for analysis of thermal systems using tools hitherto reserved for a-thermal ones, and thereby prediction of thermodynamic properties, study of stability, etc. Quite remarkably we observe the emergence of eective many-body interactions, even when the bare interactions are purely 2-body. This resolves the puzzle posed by recent studies that showed a quantitative match between 2D/3D measurements and the innite dimension mean-eld prediction.


Daniel Hexner
08/11/2017 - 10:30

As temperature is lowered, motion becomes more sluggish.  Below the glass transition temperature, the dynamics of super-cooled liquids becomes so slow that the system falls out of equilibrium.  One hypothesis for this dynamic arrest is that it is due to a thermodynamic phase transition with a diverging length scale.  However, there is scant evidence of such a length scale appearing in the structure.  Motivated by this, we study another amorphous system that undergoes a phase transition: jammed soft repulsive spheres at zero temperature.  We have discovered a subtle correlation length, associated with the local coordination of particles, that is not seen in the two-point correlation function, g(r).  We argue that this scale plays an important role in determining the local rigidity of the system, and diverges with an exponent 2/(d+1) as the jamming transition is approached.

Amir Erez ( Princeton University)
25/10/2017 - 10:30

Positive feedback in biochemical networks can lead to a bifurcation in state space. Universality implies that if molecules are well mixed, this bifurcation should exhibit the critical scaling behavior of the Ising universality class in the mean-field limit. Making this statement quantitative requires the appropriate mapping between the biochemical parameters and the Ising parameters. Here we derive this mapping rigorously and uniquely for a broad class of stochastic birth-death models with feedback, and show that the expected static and dynamic critical exponents emerge. The generality of the mapping allows us to extract the order parameter, effective temperature, magnetic field, and heat capacity from T cell flow cytometry data without needing to know the underlying molecular details. We find that T cells obey critical scaling relations and exhibit critical slowing down, and that the heat capacity determines molecule number from fluorescence data. We demonstrate that critical scaling holds even as our system is driven out of its steady state, via the Kibble-Zurek mechanism for driven critical systems. Our approach places a ubiquitous biological mechanism into a known class of physical systems and is immediately applicable to other biological data.

Gadi Afek
07/06/2017 - 10:30

In this talk I will present an experimental study of the anomalous dynamics of ultra-cold Rb atoms propagating in a 1D, dissipative, Sisyphus-type optical lattice. We find that the width of the cloud exhibits a power-law time dependence with an exponent that depends on the lattice depth. Moreover, the distribution exhibits fractional self-similarity with the same characteristic exponent. The self-similar shape of the distribution is found to be well fitted by a Lévy distribution. I will further present a measurement of the phase-space density distribution (PSDD) of the cloud of atoms. The PSDD is imaged using a direct tomographic method comprised of velocity selection and spatial imaging. We show that the position-velocity correlation function, obtained from the PSDD, decays asymptotically as a function of time with a power-law that we relate to a simple scaling theory involving the power-law asymptotic dynamics of the position and velocity. The generality of this scaling theory is confirmed using Monte-Carlo simulations of two distinct models of anomalous diffusion dynamics.


Ohad Shpielberg
17/05/2017 - 10:30
Phase transitions are of unfading interest. While classical systems in equilibrium present no phase transitions in 1 dimension, they can be manifested in systems driven out of equilibrium. In this talk we will explore the current fluctuations in boundary driven systems. Current fluctuations are explored by the probability to observe an atypical current over a long period of time. We will show a few examples of phase transitions and classify them. For a special kind of phase transitions, we will show a mapping to a single particle evolving under classical Lagrangian mechanics. This mapping  provides us with a simple picture of where one could expect such transitions.      


Eli Zeldov (Weizmann)
27/04/2017 - 12:30 - 13:30
Eli Zeldov


Sid Redner
19/02/2017 - 10:30

What is the fate of a forager that depletes its environment as it wanders? We investigate this question within the "starving" random walk model, in which the forager starves when it travels S steps without eating.  The forager consumes food whenever it is found and becomes fully sated.  However, when the forager lands on an empty site, it moves one time unit closer to starvation.  We determine the forager lifetime, analytically in one dimension and numerically in higher dimensions.  In two dimensions, long-lived walks explore a highly ramified region so as to remain close to food.

We also investigate the role of greed, in which the forager preferentially moves towards food when faced with a choice of hopping to food or to an empty site.  Paradoxically, the forager lifetime can have a non-monotonic dependence on greed, with a different sense to the non-monotonicity in one and in two dimensions.

Madhu Pryia
14/12/2016 - 10:30


Michael Nosonovsky
07/12/2016 - 10:30

Small-amplitude fast vibrations and small surface micropatterns affect properties of various systems involving wetting, such as superhydrophobic surfaces and membranes.  The mathematical method of averaging the effect of small fast vibrations is known as the method of separation of motions. The vibrations are substituted by effective force or energy terms, leading to vibration-induced phase control. The best known example of that is the stabilizationb of an inverted pendulum on a vibrating foundation (the Kapitza pendulum); however, the method can be applied to a number of various situations including wetting. A similar averaging method can be applied to surface micropatterns leading to surface texture-induced phase control. We argue that the method provides a framework that allows studying such effects typical to biomimetic surfaces, such as superhydrophobicity, membrane penetration and others. Patterns and vibration can effectively jam holes and pores in vessels with liquid, separate multi-phase flow, change membrane properties, result in propulsion, and lead to many other multiscale, non-linear effects. These effects can be used to develop novel materials.

Eial Teomy
16/11/2016 - 10:30

In a liquid all the particles are mobile, while in a glass only some of them are mobile at any given time. Although overall the structure is amorphous in both cases, the difference is that in glasses there are local structures that inhibit the movement of particles inside them. We investigate these structures by considering the minimum number of particles that need to move before a specific particle can move. By mapping the dynamics of the particles to diffusion of mobile vacancies, we find a general algebraic relation between the mean size of the structures and the mean persistence time, which is the time until a particle moves for the first time. The exponent relating these two quantities depends on the system's properties. 


We investigated this relation analytically and numerically in several kinetically-constrained models: the Fredrickson-Andersen, Kob-Andersen and Spiral models. These models are either lattice gas models or Ising-like models, in which a particle can move or a spin can flip only if the local environment satisfies some model-dependent rule. Due the discrete nature of these models and relative simplicity, we were able to analytically find the relation between the structure and the dynamics and found an excellent agreement between our analytical results, our numerical simulations, and the heuristic arguments presented above. In these simple models, the minimum number of particles that need to move before a specific particle can move is easily found by using a culling algorithm, also called bootstrap or threshold percolation.

Ohad Shpielberg
22/06/2016 - 10:30

The recently formulated macroscopic fluctuation theory is a successful  description of out of equilibrium diffusive systems. I will focus on  current fluctuations of boundary driven systems within the macroscopic  theory description, and discuss the relevance of the additivity  principle to derive the large deviation function associated with the  current fluctuations. Three results will be shown

 1) Current fluctuations in boundary driven systems are universal

 2) A criterion for the validity of the additivity principle and  application to dynamical phase transitions.

  3) Relevance of the macroscopic fluctuation theory to transport of  disordered quantum systems.

Luca Giuggioli
08/06/2016 - 10:30

Collective movement patterns appear at all scales from microorganisms to invertebrate and vertebrate animals. In certain cases the individual entities communicate indirectly modifying the environment in which they roam by leaving a trace of their action or passage. This form of interaction has a long tradition in the ecological literature and is called stigmergy. In the context of territorial mammals modification of the environment occurs because of scent deposition and is being exploited to maintain exclusive ownership of certain region of space. By introducing the so-called territorial random walkers, it is possible to study the formation of territorial patterns by modelling the movement and interaction of scent-depositing animals. Territorial random walkers consist of agents that move at random and deposit scent, that is mark the locations they visit using temporal flags that decay over a finite amount of time, and retreat upon encountering a foreign scent. Depending solely on the ratio between the time for which the mark is active and the time it takes for the walker to cover its own territory, the system displays different patterns. Short lived marks produce rapidly morphing, fast traveling territories. A broad range of shapes and territory sizes are observed, and these territories may display ergodic trajectories. Marks that remain active for long times yield slowly moving territories that resemble glassy systems. In such state territories are effectively confined in space and have a more homogeneous shape distribution. I will show how these different regimes emerge based on the population density and the length of time for which marks remain active. I will also present an adiabatic mean-field approximation that allows to describe at short times the dynamics of the walker and that of the territory boundaries through a Fokker-Planck formalism.

Yuval Zelnik
01/06/2016 - 10:30

Regime shifts in ecosystems are typically understood to be abrupt global transitions from one stable state to an alternative stable state, induced by slow environmental changes or global disturbances. However, spatially extended ecosystems often exhibit patterned states, which allows for more complex dynamics to take place. A bistability of a patterned state and a uniform state can lead to a multitude of stable hybrid states, with small domains of one state embedded in the other state. The response of the system to local disturbances or change in global parameters in these systems can lead to gradual regime shifts, involving the expansion of alternative-state domains by front propagation, rather than a global collapse. Moreover, a regime of periodic perturbations can give rise to step-like gradual shifts with extended pauses at these states. The implications of these scenarios to regime shifts in dryland vegetation will be discussed, focusing on the case of fairy circles in Namibia as a concrete example.


Prof. Thomas Witten, the Department of Physics, University of Chicago
18/05/2016 - 12:00

Atomic scale matter, like a particle with spin, can respond to external perturbations in a chiral way: the spin rotates in response to a magnetic field.  That is, a vector perturbation gives rise to an angular velocity.  The technology of pulsed nuclear magnetic resonance exploits this response to organize and manipulate a sample of initially disordered spins.  In this talk we explore the analogs of this principle in the world of colloidal matter—micron-scale solid bodies of irregular shape.  Such bodies can respond chirally to external forcing via their hydrodynamic coupling.  This chiral response is richer than that of a nuclear spin.  As with nuclear spin, this response gives a handle that can bring a randomly-oriented dispersion of colloidal objects into a common orientation.  The alignment can be created by phase locking, analogous to pulsed nuclear magnetic resonance.  It can also be created by random external perturbations.  Here the alignment principle is the phenomenon of “noise-induced synchronization” known in dynamical systems.  

Yohai Bar Sinai
30/03/2016 - 10:30

Both thermal fluctuations and material inhomogeneity/disorder play a major role in many branches of science. This talk will focus on various aspects of the interplay between the two. First, we consider the spatial distribution of thermal fluctuational energy and derive universal bounds for internal-stress-free systems. In addition, we show that in 1D systems the thermal energy is equally partitioned even among coupled degrees of freedom. Applications to severing of actin filaments and protein unfolding are discussed. Then, we consider fluctuations in residually-stressed systems and their coupling to anharmonicity. In the context of glassy systems, we show that thermal energy van be spatially localized and suggest that it might serve as a useful structural diagnostic tool, e.g. for identifying glassy lengthscales and precursors to plastic events under driving forces. Lastly, we consider the continuum approach (Statistical Field Theory) to analyzing fluctuations in inhomogeneous systems, and demonstrate fundamental discrepancies between the continuum and the discrete theories in explicit calculations of some, but not all, fluctuation-induced (Casimir-like) forces.

Shlomi Reuveni
13/01/2016 - 10:30

In 1913 Michaelis & Menten published a seminal paper in which they presented a mathematical model of an enzymatic reaction and demonstrated how it can be utilized for the analysis and interpretation of kinetic data. More than a century later, the work of Michaelis & Menten is considered classic textbook material, and their reaction scheme is widely applied both in and out of its original context. At its very core, the scheme can be seen as one which describes a generic first passage time process that has further become subject to stochastic restart. This context free standpoint is not the standard one but I will explain how it has recently allowed us to treat a wide array of seemingly unrelated processes on equal footing, and how this treatment has unified, altered, and deepened our view on single-molecule enzymology, kinetic proof-reading and complex search processes. Newly opened opportunities for theoretical and experimental research will also be discussed. 

Dr. Amir Bashan
07/01/2016 - 10:00

Our body is colonized by trillions of microbes, known as the human microbiome, 
living with us in a complex ecological system. Those micro-organisms play a crucial 
role in determining our health and well-being, and there are ongoing efforts to
develop tools and strategies to control these ecosystems.
In this talk I address a simple but fundamental question: are the microbial ecosystems 
in different people governed by the same host-independent ecological
 principles, represented by a characteristic (i.e. “universal”) mathematical model?
Answering this question determines the feasibility of general therapies and 
control strategies for the human microbiome. 
I will introduce our novel methodology that distinguishes between two scenarios: host-independent 
and host-specific underlying dynamics. This methodology has been applied to study 
different body sites across healthy subjects. The results can
fundamentally improve our understanding of forces and processes shaping human microbial 
ecosystems, paving the way to design general microbiome-based therapies.


Ankush Sengupta
06/01/2016 - 10:30
Microswimmers are microscopic objects that self-propel in a fluid. Synthetic microswimmers, designed with active colloids, propel by various driving mechanisms, for example, in response to a solute concentration gradient (diffusiophoresis), or a temperature gradient (thermophoresis), or through the manipulation of an external magnetic field. Janus colloids propelled by light, e.g., thermophoretic particles, offer promising prospects as artificial microswimmers. However, their swimming behavior and its dependence on fluid properties and fluid–colloid interactions remain poorly understood. Employing the energy-conserving dissipative particle dynamics simulations, we investigate the behavior of a thermophoretic Janus colloid in its own temperature gradient. In particular, we explore the effects of non-ideal and ideal-gas like fluids for different fluid-colloid interactions, boundary conditions and different temperature-control strategies. Given that these microswimmers need to perform in a highly fluctuating low Reynolds number world, our study brings forth the factors that can modify and control their dynamics. 
Anna Bordova
23/12/2015 - 10:30

Brownian motion with time-dependent diffusion coefficient is ubiquitous in nature. It has been observed for the mobility of proteins in cell membranes, motion of molecules in porous environment, water diffusion in brain measured in terms of magnetic resonance imaging and also in media with time-dependent temperature such as free cooling granular materials or melting snow.

We investigate a new type of anomalous diffusion processes governed by an underdamped Langevin equation with time-dependent diffusion and friction coefficients and discuss possible applications to real physical systems such as free cooling granular materials. We show that for certain range of parameter values the overdamped limit for the Langevin equation does not exist.

Dino Osmanovi
19/08/2015 - 10:30

 We study the random bond lattice model in which the strength

of the bond between any two neighboring particles is randomly chosen such

that each of N  particles is characterized by N

Jonathan Selinger
29/04/2015 - 10:30

We investigate the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.

Fyl Pincus
16/03/2015 - 14:00

For over 90 years there has been an unexplained puzzle associated with the viscosity of dilute aqueous salt solutions. More specifically, there is a contribution to the viscosity which is linear in the salt concentration and very ion specific for monovalent salts. This is usually discussed in terms of the Jones-Dole coefficient (B) which is the amplitude of the linear term in the concentration. The A coefficient was derived by Falkenhagen and Onsager many years ago in terms of the Debye-Hückel theory for electrolytes. We shall discuss our current understanding of the Jones-Dole coefficient in the context of ionic hydration.  

Haim Weisman
04/02/2015 - 10:30
The process of desertification is usually modeled as a first-order transition, where a change of an external parameter (e.g., precipitation) leads to a catastrophic  bifurcation followed by an ecological regime shift. However, vegetation elements like shrubs and trees undergo a stochastic birth-death process with an absorbing state; such a process supports a second-order continuous transition with no hysteresis. Here we study a minimal model of a first-order transition with an absorbing state. When the external parameter varies adiabatically the transition is indeed continuous, and we present some empirical evidence that supports this scenario. The front velocity renormalizes to zero at the extinction transition, leaving a finite "quantum" region where domain walls are stable and the desertification takes place via accumulation of local extinctions. A catastrophic regime shift may occur as a dynamical hysteresis, if the pace of environmental variations is too fast. Due to this work we suggest that the focus of searching early-warning signals should be related to the extinction transition, where large nuclei of bare soil may invade the vegetation phase. Furthermore, we suggest that tracking patch dynamics one can differentiate between continuous and discontinuous (catastrophic shift) types of transition.
Daphne Weihs
31/12/2014 - 10:30

Mechanics of cancer cells are directly linked to their metastatic potential (MP), or ability to produce a secondary tumor at a distant site. Metastatic cells can squeeze through blood vessel walls and tissue. Such considerable structural changes rely on rapid remodeling of internal cell structure and mechanics. We perform a comparative study, using particle-tracking to evaluate the intracellular mechanics of living epithelial breast cells with varying invasiveness. Probe-particle transport differs between the cell types, likely relating to their cytoskeleton network-structure and underlying transport. The basic analysis included evaluation of the time-dependent mean square displacement (MSD), the second power of the displacement. Particles in all the evaluated cell lines exhibit anomalous super-diffusion with an MSD scaling exponent of 1.4, at short lag times below 1 second. While indicating active transport within the cells, the MSD alone cannot reveal the underlying mechanisms. Hence, we analyze particle motion through a combination the MSD, other powers of the displacement, and various trajectory and displacement analysis procedures to identify structural and dynamic changes associated with metastatic capabilities of cells.

The dynamic cytoskeleton and especially the molecular motors acting on it provide the cell with its remodeling capabilities and allow active transport within the cell. While active transport in living cells has been well-documented, the underlying mechanisms have not been determined. Here, we systematically target the cytoskeleton, molecular motors, and ATP energy related processes to determine their roles in particle transport. Our results show that particle motion is likely driven by different processes in each cell type. Intracellular transport in high MP cells is suggested to originate from fluctuations of microtubule filaments as well as from direct and indirect interactions between particles and microtubule-associated molecular motors. In the low MP cells we suggest that motion results from direct and indirect interactions between particles and microtubule-associated molecular motors, being transported by them or nudged by passing motors, respectively. The benign cells, however, reveal significant involvement of the acto-myosin network, where particle motion was related to network contractions. Thus, we are able to provide insight into dynamic intracellular structure and mechanics that can support the unique function and invasive capabilities of highly metastatic cells.

Igor Sokolov
24/12/2014 - 10:30

We discuss models of anomalous diffusion (mostly subdiffusion) in complex systems on the different levels of description and try to classify different types of the behavior. We moreover introduce statistical tests which allow to distinguish between different classes of such models and between different models within the class on the level of ensembles of the trajectories and of the single trajectories of the corresponding processes.

Lenin Shagolsem
17/12/2014 - 10:30

Inspired by biological systems in which thousands of different types of proteins interact within a cell, we use molecular dynamics simulations in 2d to study multi-component systems in the large number of species limit, i.e., all particles differ from each other (APD systems). All the particles are assumed to be of the same size and interact via the Lennard-Jones (LJ) potential, but their pair interaction parameters are generated at random from a uniform or a peaked distribution. We analyze both the global and the local properties of these systems at temperatures above the freezing transition and find that APD fluids relax into a self-organized state characterized by clustering of particles according to the values of their pair interaction parameters. 

Johannes Schulz
03/12/2014 - 10:30

I discuss the occupation time statistics in thermal, ergodic continuous-time random walks. While the average occupation time is given by the canonical Boltzmann-Gibbs law from Statistical Physics, the finite-time fluctuations around this mean turn out to be large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations.

Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas.

Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and stable densities of fluctuations.

Itzhak Fouxon
19/11/2014 - 10:30

 We study the sequence of particles' collisions in a small system of hard balls. We demonstrate that ergodicity implies quite unusual phenomenon. The particles have preferences over long time intervals during which the particle consistently collides more with certain particles and less with others. Things look like there is effective interaction between the particles. Though the preferences change sooner or later the average waiting time to the change is infinite. The results hold for dilute gas with arbitrary short-range interactions and dense fluids of hard balls.