In nature, insects, fish, birds and other animals flock. A simple two-dimensional model due to Vicsek et al treats them as self-propelled particles that move with constant speed and, at each time step, tend to align their velocities to an average of those of their neighbors except for an alignment noise (conformist rule). The distribution function of these active particles satisfies a kinetic equation. Flocking appears as a bifurcation from an uniform distribution of particles whose order parameter is the average of the directions of their velocities (polarization). This bifurcation is quite unusual: it is described by a system of partial differential equations that are hyperbolic on the short time scale and parabolic on a longer scale. Uniform solutions provide the usual diagram of a pitchfork bifurcation but disturbances about them obey the Klein-Gordon equation in the hyperbolic time scale. Then there are persistent oscillations with many incommensurate frequencies about the bifurcating solution, they produce a shift in the critical noise and resonate with a periodic forcing of the alignment rule. These predictions are confirmed by direct numerical simulations of the Vicsek model. In addition, if the active particles may choose with probability p at each time step to follow the conformist Vicsek rule or to align their velocity contrary or almost contrary to the average one, the bifurcations are of either period doubling or Hopf type and we find stable time dependent solutions. Numerical simulations demonstrate striking effects of alignment noise on the polarization order parameter: maximum polarization length is achieved at an optimal nonzero noise level. When contrarian compulsions are more likely than conformist ones, non-uniform polarized phases appear as the noise surpasses threshold.
Peter Morse : Generic failure in granular packings: finding the relationship between shear and random forces- Uploaded by root ( 128 Views )
Under shear, a jammed packing of particles will break in characteristic ways and transition between mechanically stable states. One can then ask whether the signatures of failure are specific to shear, or whether they are the same in more generic perturbations. Interestingly, recent mean-field calculations suggest that in infinite dimensions, the response of a system to global shear and random forces may be equivalent. Whether or not this is true in 2D or 3D systems remains an open question. Therefore, I've developed a method for driving 2D jammed packings of disks by quasti-static persistent random forces to demonstrate that the response is similar to what is observed in athermal quasi-static shear simulations. I will also comment on how we expect the similarities to break in finite dimensions and what these results might imply for active matter systems.
Understanding the self-organization principles and collective dynamics of non-equilibrium matter remains a major challenge despite considerable progress over the last decade. In this talk, I will introduce a hydrodynamic analog system that allows us to investigate simultaneously the wave-mediated self-propulsion and interactions of effective spin degrees of freedom in inertial and rotating frames. Millimetric liquid droplets can walk across the surface of a vibrating fluid bath, self-propelled through a resonant interaction with their own guiding wave fields. A walking droplet, or `walker, may be trapped by a submerged circular well at the bottom of the fluid bath, leading to a clockwise or counter-clockwise angular motion centered at the well. When a collection of such wells is arranged in a 1D or 2D lattice geometry, a thin fluid layer between wells enables wave-mediated interactions between neighboring walkers. Through experiments and mathematical modeling, we demonstrate the spontaneous emergence of coherent droplet rotation dynamics for different types of lattices. For sufficiently strong pair-coupling, wave interactions between neighboring droplets may induce local spin flips leading to ferromagnetic or antiferromagnetic order. Transitions between these two forms of order can be controlled by tuning the lattice parameters or by imposing a Coriolis force mimicking an external magnetic field. More generally, our results reveal a number of surprising parallels between the collective spin dynamics of wave-driven droplets and known phases of classical condensed matter systems. This suggests that our hydrodynamic analog system can be used to explore universal aspects of active matter and wave-mediated particle interactions, including spin-wave propagation and topologically protected dynamics far from equilibrium.
The idea that glasses can become marginally stable at a Gardner transition has attracted significant interest among the glass community. Yet, the situation is confusing: even at the theoretical level, renormalization group approaches provide contradictory results on whether the transition can exist in three dimensions. The Gardner transition was searched in only two experimental studies and few specific numerical models. These works lead to different conclusions for the existence of the transition, resulting in a poor understanding of the conditions under which a marginally stable phase can be observed. The very relevance of the Gardner transition for experimental glasses is at stake.
We study analytically and numerically the Weeks-Chandler-Andersen model. By changing external parameters, we continuously explore the phase diagram and regimes relevant to granular, colloidal, and molecular glasses. We revisit previous numerical studies and confirm their conclusions. We reconcile previous results and rationalise under which conditions a Gardner phase can be observed. We find that systems in the vicinity of a jamming transition possess a Gardner phase. Our findings confirm the relevance of a Gardner transition for colloidal and granular glasses, and encourage future experimental work in this direction. For molecular glasses, we find that no Gardner phase is present, but our studies reveal instead the presence of localised excitations presumably relevant for mechanical and vibrational properties of glasses.
Granular materials are a part of a broad class of amorphous materials that display yield stress behavior. When the applied shear stress is below the yield stress, grains move temporarily, but only until finding a mechanically stable (MS) configuration that is able to resist the applied shear stress. Above the yield stress, the material is no longer able to find MS configurations. However, the geometrical reasons why MS states vanish at the yield stress is not well understood. In this talk, I will show evidence from molecular dynamics simulations that yielding in granular materials is akin to a second-order critical point, where the mechanical behavior is dominated by a correlation length that diverges at the yield stress. MS states exist above the yield stress for finite systems, but they vanish as the system size becomes large according to a critical scaling function. The packing fraction and coordination number for MS states are independent of the applied shear stress, implying that the critical behavior we observe is distinct from the well known jamming scenario. However, MS states at nonzero shear stress possess anisotropic force and contact networks, suggesting that the yield stress is set by the maximum anisotropy that can be realized in the large-system limit.
Studying how small inertial particles suspended in turbulent flows
move relative to each other provides fundamental insights into their
transport, mixing and collisions. These insights are crucial for
tackling diverse problems ranging from droplet growth in warm clouds,
to planetesimal formation through collisional aggregation in turbulent
protoplanetary nebula. A deeper understanding of the relative motion
of the particles can be obtained by investigating both their
forward-in-time (FIT) and backward-in-time (BIT) dispersion. When FIT
and BIT dispersion are different it signifies irreversibility, and
since FIT and BIT dispersion are related to different problems,
understanding the irreversibility is of fundamental and practical
I will present new theoretical arguments and asymptotic predictions, along with results from Direct Numerical Simulations (DNS) of the governing equations, to show that inertial particle dispersion can be very strongly irreversible in turbulence, with BIT being much faster than FIT dispersion in 3-dimensional turbulence. The results also show that inertial particles can disperse much faster than fluid (interialess) particles. I will also present arguments, confirmed by DNS results, that in 2-dimensional turbulence the nature of the irreversibility and the direction of the particle energy fluxes can invert when the particle inertia exceeds a certain threshold. These results significantly advance our understanding of dispersion problems, and lead to new capabilities for predicting the effect of inertia on the rate at which particles spread out and mix together in turbulence, and the rate at which they collide.
Bryan J. Glaz : The Quasi-Periodic Intermittency Attractor and a Fractional Calculus Perspective of Generalized Spectral Decompositions for Nonlinear Dynamical Systems- Uploaded by root ( 108 Views )
Complex, nonlinear dynamical systems are pervasive across many Army relevant scientific disciplines, including turbulence, robotics, and reconfigurable active matter. Typically, our engineering objectives are to control the
dynamics. However, our inability to achieve these objectives for a variety
of high-dimensional dynamical systems is due to a lack of mathematical tools
to describe underlying salient, particularly when it comes to control of
such systems. This talk focuses on the Koopman theoretic based spectral
decomposition perspective for extracting these features.
In the first part of the talk, we demonstrate how external forcing (e.g. control) can be accounted for in the form of a parametric term added to the Koopman operator of the unforced system. By using the simple fluid dynamics example of streamwise oscillating flow over a cylinder, we establish an analogy with parametrically excited Hopf bifurcations. Quite unexpectedly, we happened upon a peculiar phenomenon that is not quite chaotic, not quite quasi-periodic, and not quite intermittent. We establish the theoretical underpinnings for this phenomenon, that we name Quasi-periodic Intermittency and we discuss the implications across a variety of physical systems. In the second part of the talk, a fractional calculus perspective of complexity will be introduced to generalize Koopman based spectral decompositions to systems with memory as a first step toward dealing with truly complex systems. The analysis leads to modes whose temporal behavior is anomalous and lacks a characteristic scale. The approach we propose may uncover inherent memory effects that would otherwise be obscured by conventional spectral methods.
The talk will conclude with a discussion of new follow-on research thrusts ranging from control for adaptive, reflexive robotic mobility to self-organized adaptation and reconfiguration of active matter systems. In addition, opportunities for students (undergraduate and graduate) and faculty to engage with the U.S. Army Research Laboratory will be discussed.
Stephen Teitel : Shear Banding, Discontinuous Shear Thickening, and Rheological Transitions in Athermally Sheared Frictionless Disks- Uploaded by root ( 114 Views )
Simple models of classical particles, interacting via soft- or hard-core repulsive contact interactions, have been used to model a wide variety of granular and soft-matter materials, such as dry granular particles, foams, emulsions, non-Brownian suspensions, and colloids. Such materials display a variety of complex behaviors when in a state of steady shear driven flow. These include (i) Jamming: where the system transitions from a flowing liquid to a rigid but disordered solid as the particle packing increases; (ii) Shear Banding: where the system becomes spatially inhomogeneous, separating into distinct bands flowing at different sh ear strain rates; (iii) Discontinuous Shear Thickening: where the shear stress jumps discontinuously as the shear strain rate is increased. In this talk we will consider a simple numerical model of athermal soft-core interacting frictionless disks in steady state shear flow. We will show that the mechanism by which energy is dissipated plays a key role in determining the rheology of the system. For a model with a tangential viscous collisional dissipation, but no elastic friction, we will show that as the particle packing increases there is a sharp first order phase transition from a region of Bagnoldian rheology (stress ~ strain-rate^2) to a region of Newtonian rheology (stress ~ strain-rate), that takes place below the jamming transition. In a phase diagram of varying strain-rate and packing fraction (or strain-rate and pressure) this first order rheological phase transition manifests itself as a coexistence region, consisting of coexisting bands of Bagnoldian and Newtonian rheology in mechanical equilibrium with each other. Crossing this coexistence region by increasing the strain-rate at fixed packing, we find that discontinuous shear thickening can result if the strain-rate is varied too rapidly for the system to relax to the true shear-banded steady state. We thus demonstrate that the rheology of simply interacting sheared disks can be considerably more complex than previously realized, and our model suggests a simple mechanism for both the phenomena of shear banding and discontinuous shear thickening in spatially homogeneous systems, without the need to introduce elastic friction.
Cells exist in a complex mechanical environment that is both a source of applied forces and a means of mechanical support. An incomplete understanding of the mechanisms cells use to detect mechanical stimuli, a process termed mechanotransduction, is currently preventing advances in tissue engineering and hindering the understanding of several mechanosensitive disease states. Mechanical stimuli are sensed at focal adhesions (FAs), complex dynamic structures comprised of several hundred types of proteins that mediate physical connections between the extracellular matrix and the cytoskeleton. Detection of mechanical cues is thought to be mediated by mechanically-induced changes in protein structure, which, in elegant in vitro single molecule experiments, have been shown to induce new biochemical functions, such as changes in binding affinity as well as the formation of distinct protein-protein interactions. However, the existence and role of these mechanically-induced changes in protein function in living cells are not well understood. To enable the visualization of protein loading, we create Forster Resonance Energy Transfer (FRET)-based tension sensors that emit different colors of light in response to applied forces. The next step in the development of this technology is the use of these sensors to study the effects of mechanical loading on protein functions in living cells. To begin this process, we have refined two commonly used and powerful approaches, Fluorescence Recovery After Photobleaching (FRAP) and fluorescence co-localization to be compatible with FRET-based tension sensors. Initial efforts have focused on the mechanical linker protein vinculin due to its established role in regulating the response of FAs to mechanical loading. These novel techniques reveal that force affects both vinculin turnover as well as its ability to form distinct protein-protein interactions. Further use of these techniques should enable a wide variety of studies in mechanobiology involving different load-bearing proteins, subcellular structures, extracellular contexts, and cellular functions.
Living organisms need to obtain and process information crucial for their survival. Information processing in living systems, ranging from signal transduction in a single cell to image processing in the human brain, are performed by biological circuits (networks), which are driven out of equilibrium. These biochemical and neural circuits are inherently noisy. However, certain accuracy is required to carry out proper biological functions. How do biological networks process information with noisy components? What is the free energy cost of accurate biological computing? Is there a fundamental limit for its performance of the biological functions? In this talk, we will describe our recent work in trying to address these general questions in the context of two basic cellular computing tasks: sensory adaptation for memory encoding [1,2]; biochemical oscillation for accurate timekeeping .
 The energy-speed-accuracy trade-off in sensory adaptation, G. Lan, P.
Sartori, S. Neumann, V. Sourjik, and Yuhai Tu, Nature Physics 8, 422-428,
 Free energy cost of reducing noise while maintaining a high sensitivity, Pablo Sartori and Yuhai Tu, Phys. Rev. Lett. 2015. 115: 118102.
 The free-energy cost of accurate biochemical oscillations, Y. Cao, H. Wang, Q. Ouyang, and Yuhai Tu, Nature Physics 11, 772, 2015.
Ana Barros : Down the Predictability Hole - Searching for Metrics to Understand and Replace Physical Parameterizations of Nonlinear Processes in Atmospheric Models- Uploaded by root ( 120 Views )
Short-term forecast skill in weather forecasting over the last 15 years has been achieved mostly through data assimilation. Predictive ability however has hit barriers that have not been overcome by increasing computer power and model resolution. Model tuning has come out from hiding, and it is arguably ``trending'' in peer-review over the last 2-3 years. The open question is what (and how) to do next. I will address this question relying on two-decades of research on the representation of moist processes in the atmosphere, specifically targeting the following issues: 1) Evaluating Models to Elucidate the Physics that Matter 2) Detecting and Isolating Sources, Sinks and Barriers of Predictability 3) Meeting the Utility Challenge - Projections vs Predictability
Many systems of interest can be represented by a network of nodes connected by edges. In many circumstances the existence of a giant component is necessary for the network to fulfill its function. Motivated by the need to understand optimal attack strategies, optimal spread of information or immunization policies, we study the network dismantling problem, i.e. the search of a minimal set of nodes whose removal leaves the network broken into components of sub-extensive size. Building on the statistical mechanics perspective we compute the size of the optimal dismantling set for random networks, propose an efficient dismantling algorithm for general networks that outperforms by a large margin existing strategies, and we provide various insights about the problem.
Maciej Balajewicz : Nonlinear dimensionality reduction: from turbulent fluid flows to computational finance- Uploaded by root ( 112 Views )
The past several decades have seen an exponential growth of computer processing speed and memory capacity. The massive, complex simulations that run on supercomputers allow exploration of fields for which physical experiments are too impractical, hazardous, and/or costly. Accurate and efficient high-fidelity simulations are critical to many energy, defense, and health applications, e.g., global climate simulations, optimal design of wind systems for power generation, combustion simulations aimed at increasing fuel efficiency and reducing carbon emissions, simulations of heart fibrillation, and many others. Unfortunately, even with the aid of massively parallel next-generation computers, high-fidelity simulations are still too expensive for real-time and multi-query applications such as uncertainty quantification, design, optimization, and control. For this reason, interest in model order reduction continues to grow. In this talk I will summarize recent advances in nonlinear model reduction for high-Reynolds-number fluid flows, structural dynamics, and computational finance.
Over the past decade, much attention has focused on the behavior of hydrophobic particles at interfaces. These systems are of interest to scientists and engineers, for example, due to their potential for stabilizing drops and emulsions via jamming. This seminar will focus on the behavior of particulate 'rafts' that form when a monolayer of particles are placed at an air- liquid interface. The particles interact with the underlying fluid to form a quasi two-dimensional solid. Such particulate rafts can support both tension and compression, and they buckle under sufficiently large compressive loads. When a drop of surfactant is introduced into the system, fracture networks develop in the rafts. The fracture process exhibits features observed in other elastic systems, such as crack kinking, crack branching, and crack arrest. Moreover, there is a clear coupling between the praft fracture and the diffusion of the surfactant on the surface and through the 'porous' liquid-particle monolayer. As such, one can draw analogies between this system and others where crack growth interacts with fluid flow or mass transport. The seminar will present recent work in modeling the diffusion of surfactant into particle raft systems and the resulting formation of fracture networks. We will present both discrete models that track the motion of individual particles, as well as a new continuum model for poro-chemo-elasticity. Results that reproduce some of the quantitative and qualitative aspects of recent experimental studies of these systems will also be shown.
Brains have an impressive ability to store information about the external world on time scales that range from seconds to years. The rules of information storage in neuronal circuits are the subject of ongoing debate. Two scenarios have been proposed by theorists: In the first scenario, specific patterns of activity representing external stimuli become fixed point attractors of the dynamics of the network. In the second, the network stores sequences of patterns of network activity so that when the first pattern is presented the network retrieves the whole sequence. In both scenarios, the correct dynamics are achieved thanks to appropriate changes in network connectivity. I will describe how methods from statistical physics can be used to investigate the storage capacity of such networks, and the statistical properties of network connectivity that optimizes information storage (distribution of synaptic weights, probabilities of specific network motifs, degree distributions, etc) in both scenarios. Finally, I will compare the theoretical results with available data on cortical connectivity.
We are customarily taught to understand ordinary solids by considering perturbations about a perfect crystal. This approach becomes increasingly untenable as the amount of disorder in the solid increases; for a glass with no well-defined long-range order, a crystal is a terrible starting point for understanding the glasss rigidity or its excitations. Is there an alternative the opposite of a crystal where order, rather than disorder is the perturbation? Jamming is an alternate way of creating rigid solids that are qualitatively different from crystals. In a crystal with only one atom per unit cell, all atoms play the same role in producing the solid's global response to external perturbations. Jammed disordered materials are not similarly constrained and a new principle emerges: independence of bond-level response. Using networks where individual bonds can be successively removed, one can drive the overall system to different regimes of behavior. Consequently one can exploit disorder to achieve unique, varied, textured and tunable global response.
5-8 % of the global human CO2 production comes from the production of
cement, concrete main binder. The material strength emerges through the
development, once in contact with water, of calcium-silicate-hydrate (C-S-H)
gels that literally glue together the final compound. Current industrial
research aims at exploring alternative and more environmentally friendly
chemical compositions while enhancing rheology and mechanics, to overcome
the many technological challenges and guarantee concrete standards.
Identifying the fundamental mechanisms that control the gel properties at
the early stages of hydration and setting is crucial, although challenging,
because of far-from-equilibrium conditions, closely intertwined to the
evolution of the chemical environment, that are a hallmark of cement
I will discuss a recently developed statistical physics approach, which allows us to investigate the gel formation under the out-of-equilibrium conditions typical of cement hydration and the role of the nano-scale structure in C-S-H mechanics upon hardening. Our approach, combining Monte Carlo and Molecular Dynamics simulations, unveils for the first time how some distinctive features of the kinetics of cement hydration can be related to the nano-scale effective interactions and to the changes in the morphology of the gels. The novel emerging picture is that the changes of the physico-chemical environment, which dictate the evolution of the effective interactions, specifically favor the gel formation and its continuous densification. Our findings provide new handles to design properties of this complex material and an extensive comparison of numerical findings for the hardened paste with experiments ranging from SANS, SEM, adsorption/desorption of N2 and water to nano-indentation provide new, fundamental insights into the microscopic origin of the properties measured.
K. Ioannidou, R.J.-M. Pellenq and E. Del Gado Controlling local packing and growth in calcium-silicate-hydrate gels
E. Del Gado, K. Ioannidou, E. Masoero, A. Baronnet, R. J.-M. Pellenq, F. J. Ulm and S. Yip, A soft matter in construction - Statistical physics approachfor formation and mechanics of C--S--H gels in cement,
K. Ioannidou, K.J. Krakowiak, M. Bauchy, C.G. Hoover, E. Masoero, S. Yip, F.-J. Ulm, P. Levitz, R.J.-M. Pellenq and E. Del Gado, The mesoscale textureof cement hydrates
K. Ioannidou, M. Kanduc, L. Li, D. Frenkel, J. Dobnikar and E. Del Gado, The crucial effect of early-stage gelation on the mechanical properties of cement hydrates , under review
The rheology of dense flows of hard particles is singular near the jamming threshold where flow ceases, both for aerial granular flows dominated by inertia, and for over-damped suspensions. At the same time, the length scale characterizing velocity correlations appears to diverge at jamming. We introduce a theoretical framework that proposes a potentially complete scaling description of stationary flows of frictionless particles. We compare our predictions with the empirical literature, as well as with new numerical data. Overall we find a very good agreement between theory and observations. Finally, we use simulations of frictional inertial flow to outline the regime of the phase diagram where the theory holds, and show where friction adds new physics.
The fields of evolution and population genetics are undergoing a renaissance, due to the abundance of sequencing data. On the other hand, the existing theories are often unable to explain the experimental findings. It is not clear what sets the time scales of evolution, whether for antibiotic resistance, an emergence of new animal species, or the diversification of life. The emerging picture of genetic evolution is that of a strongly interacting stochastic system with large numbers of components far from equilibrium. In this talk, I plan to focus on the clone competition and discuss the diversity of a random population that undergoes selection and recombination (sexual reproduction). Recombination reshuffles genetic material while selection amplifies the fittest genotypes. If recombination is more rapid than selection, a population consists of a diverse mixture of many genotypes, as is observed in many populations. In the opposite regime, selection can amplify individual genotypes into large clones, and the population reaches the so-called "clonal condensation". I hope to convince you that our work provides a qualitative explanation of clonal condensation. I will point out the similarity between clonal condensation and the freezing transition in the Random Energy Model of spin glasses. I will conclude with a summary of our present understanding of the clonal condensation phenomena and describe future directions and connections to statistical physics.
For centuries, origami, the Japanese art of paper folding, has been a powerful technique for transforming two dimensional sheets into beautiful three dimensional sculptures. Recently, origami has made its foray into a new realm, that of physics and engineering, where it has been revolutionizing our concept of materials design. In this talk I will describe the new design principles we are uncovering for determining the shape, mechanics, and transformations of origami structures along with their usefulness in areas as diverse as solar sail design, architecture, and even fashion. Arguably however, the greatest strength of this new paradigm is the fact that origami is intrinsically scalable. Thus sculptures built at one size can be shrunk down smaller and smaller. This begs the question: what is the smallest fold one can make? Or in other words, how many folded angels can dance on the head of a pin? The rest of this talk will take a deep dive into how origami has been marching smaller and smaller in size. From folding by hand, to self-folding through shape memory alloys and even folding via polymer layers, I will argue that the ultimate limit for scaling down origami is set by folding a sheet of atomic dimensions. I will conclude by showing this vision: realized in the folds of a single sheet of graphene.
Glasses (aka amorphous solids) exhibit various anomalies when compared with crystals (aka ordered solids), for instance, they display enhanced transport, activated slow dynamics across energy barriers, excess vibrational modes with respect to Debye's theory (the so-called Boson Peak) or respond drastically to very small mechanical deformations. In this work, we identify the common, universal origin to these anomalies in a realistic, three-dimensional model of glasses. We show that in highly packed hard spheres, vibrations become highly correlated in space and time at a sharply defined threshold, which we call the "Gardner threshold". This work is deeply related with the last developments in the analytical theory of glasses, where the glass problem has been finally solved exactly in the artificial limit of infinite spatial dimensions. The analytical solution predicts the existence of a genuine phase transition (a Gardner phase transition) within the glass, separating the glass and the jamming transitions. In this work we, not only establish the relevance of the (remanent of the) Gardner transition for real glasses, but also characterize it using well-defined observables, including time-dependent quantities and spatial correlations, that should be experimentally measurable. See arxiv.org/abs/1511.04201
Upon approaching the glass transition a liquid gets extremely sluggish without obvious structural changes. Despite decades of work, the physical origin of this glassy slowdown remains controversial. A common explanation relies on the increasing roughness of the underlying free-energy landscape, but the theoretical and experimental underpinnings of this scenario are still lacking. In this talk, I will survey recent advances that let us unambiguously identify and track the growing amorphous order, a manifestation of the rarefaction of metastable states in the rugged landscape. I will further explore the crucial role this order plays in driving the glassy slowdown.
The cohesive strength of granular materials is a consequence of either cohesive bonding (capillary bridging, van der Waals forces) between the grains or the action of a binding solid or liquid material in the pore space. I first discuss the constitutive framework of the plastic behavior of granular materials with internal variables pertaining to the granular fabric. Then, I show how cohesive granular systems can be simulated by different methods accounting for capillary or solid bonding and in the presence of a binding solid or liquid. Finally, I focus on two issues: (1) How does local granular disorder affects the scale-up of cohesive interactions? (2) What are the respective roles of adhesion and volume fraction in the case of binding materials?
Recently, the development of specialized techniques in mathematics known as
exponential asymptotics has led to the successful resolution of
long-standing problems in topics as varied as crystal growth, dislocations,
pattern formation, turbulence, thin film flow, and hydrodynamics. These
developments have emerged from the realization that in many such problems,
exponentially small effects can significantly change the solutions of the
underlying mathematical models.
In this talk, we will introduce the audience to the history, ideas, and basic techniques of exponential asymptotics, with particular emphasis on how to recognize when such approaches are necessary. We will discuss the 19th century struggles of the great Cambridge physicist G.G. Stokes to better understand what is now known as the Stokes Phenomenon. We will then show how this understanding would provide the key insight into resolving two famous problems: the problem of modelling dendritic crystal growth, and the Saffman-Taylor viscous fingering problem.
Our discussion will conclude with a glimpse of the present and future applications of exponential asymptotics, notably within the context of hydrodynamics and ship waves, and for the mathematical modelling of rupture and singularity formation in fluid flows.
Diffusion over a network depends crucially on the pattern and timing of relations. This is particularly important for diseases carried over networks with relatively low volume and turnover. Here we explore both aspects using simulation tools. First, we ask how the shape of the distribution of number of partners affects multiple connectivity, and second we measure the exposure potential in dynamic networks across a wide array of structural patterns to identify the influence of "concurrency," the overlap in time of interactions among network nodes. We find that concurrency in low-volume settings has the same effect on epidemic spreading as a structural increase in the average degree.
The glass problem is notoriously hard, but the recent exact solution of a microscopic model offers a novel perspective on the problem. In this seminar, I will discuss how contrasting entropic caging and isostaticity at the glass and the jamming transitions, respectively, reveals the presence of a Gardner transition. This onset of mechanical marginality then explains the presence of non-trivial critical exponents. I will also discuss how a family of finite-dimensional models reveals the clear role for caging geometry and hopping in the dynamical slowdown of colloid-like glass formers. Both advances greatly enrich the traditional mean-field description of glasses.
Developing descriptive and predictive models of human behavior and decision making in complex sociotechnical systems is critical for system design and evaluation. However, developing such models is difficult due to individual variability, brittle assumptions, and the need to often integrate qualitative and quantitative data. This talk will discuss various human-systems modeling techniques developed in the Humans and Autonomy Laboratory.