Memory formation in matter is a theme of broad intellectual relevance; it sits at the interdisciplinary crossroads of physics, biology, chemistry, and computer science. Memory connotes the ability to encode, access, and erase signatures of past history in the state of a system. Once the system has completely relaxed to thermal equilibrium, it is no longer able to recall aspects of its evolution. Memory of initial conditions or previous training protocols will be lost. Thus many forms of memory are intrinsically tied to far-from-equilibrium behavior and to transient response to a perturbation. This general behavior arises in diverse contexts in condensed matter physics and materials: phase change memory, shape memory, echoes, memory effects in glasses, return-point memory in disordered magnets, as well as related contexts in computer science. Yet, as opposed to the situation in biology, there is currently no common categorization and description of the memory behavior that appears to be prevalent throughout condensed-matter systems. Here we focus on material memories. We will describe the basic phenomenology of a few of the known behaviors that can be understood as constituting a memory. We hope that this will be a guide towards developing the unifying conceptual underpinnings for a broad understanding of memory effects that appear in materials.

When deformed beyond their elastic limits, crystalline solids flow plastically via particle rearrangements localized around structural defects. Disordered solids also flow, but without obvious structural defects. We link structure to plasticity in disordered solids via a microscopic structural quantity, “softness,” designed by machine learning to be maximally predictive of rearrangements. Experimental results and computations enabled us to measure the spatial correlations and strain response of softness, as well as two measures of plasticity: the size of rearrangements and the yield strain. All four quantities maintained remarkable commonality in their values for disordered packings of objects ranging from atoms to grains, spanning seven orders of magnitude in diameter and 13 orders of magnitude in elastic modulus. These commonalities link the spatial correlations and strain response of softness to rearrangement size and yield strain, respectively.

At the microscopic level, plastic flow of a jammed, disordered material consists of a series of particle rearrangements that cannot be reversed by subsequent deformation. An infinitesimal deformation of the same material has no rearrangements. Yet between these limits, there may be a self-organized plastic regime with rearrangements, but with no net change upon reversing a deformation. We measure the oscillatory response of a jammed interfacial material, and directly observe rearrangements that couple to bulk stress and dissipate energy, but do not always give rise to global irreversibility.

Out-of-equilibrium disordered systems may form memories of external driving in a remarkable fashion. The system "remembers" multiple values from a series of training inputs yet "forgets" nearly all of them at long times despite the inputs being continually repeated. Here, learning and forgetting are inseparable aspects of a single process. The memory loss may be prevented by the addition of noise. We identify a class of systems with this behavior, giving as an example a model of non-brownian suspensions under cyclic shear.Systems render information about their formation inaccessible to observers after they relax to equilibrium; a system that has not fully relaxed has the potential to retain memories of its creation. Such behavior raises questions about the type and amount of information preserved, as well as the basic operations of memory: imprinting, reading and erasure of information. Here we describe a class of systems that combine storage, reading, and loss in a single, uniform process. In the short term, these systems form concurrent memories of multiple external driving parameters. However, with no change in the driving, the systems gradually eliminate this information, selecting only one or two input values to be preserved at long times. With the addition of noise, all memories can be retained indefinitely.Such surprising behavior had first been found in a model of electronic transport by sliding charge-density waves [1,2]. However, it was not clear whether this memory formation is unique to that system or if it is an example of a more generic phenomenon. When a charge-density wave is driven across a sample by a series of discrete voltage pulses, each of the same duration A, the current response eventually becomes phaselocked to the end of each pulse [3,4]. The response therefore reveals information about the training history. This "pulse-duration memory" depends only on the driving with no fine-tuning of parameters. This behavior was modeled as self-organization of the charge-density wave around random defects in the material [5]. Further work modeled the behavior of the system when M pulse durations (A 1 ,A 2 . . . A M ) were applied in an arbitrary, repeating pattern and showed that the system learns all these inputs at intermediate times [1,2]. However, as the learning progresses, most of the responses diminish, until eventually only two memories remain. If noise is added, all the memories persist indefinitely.Since that work, this memory formation has remained unique to charge-density waves; despite the ubiquity of cyclically driven disordered systems, no one has addressed if multiple transient memory formation could be generic. Here we show that it is. A commonly observed phenomenon, not previously interpreted in terms of memory formation, has similar behavior to the multiplepulse-duration memory in charge-density waves. Our finding thus points to a new class of memory in disordered systems.When a disordered system, e.g. foam, granular material, or suspension, undergoes oscillatory shear, the indivi...

The question of how a disordered material's microstructure translates into macroscopic mechanical response is central to understanding and designing materials like pastes, foams and metallic glasses. Here, we examine a 2D soft jammed material under cyclic shear, imaging the structure of ∼ 5 × 10 4 particles. Below a certain strain amplitude, the structure becomes conserved at long times, while above, it continually rearranges. We identify the boundary between these regimes as a yield strain, defined without rheological measurement. Its value is consistent with a simultaneous but independent measurement of yielding by stress-controlled bulk rheometry. While there are virtually no irreversible rearrangements in the steady state below yielding, we find a largely stable population of plastic rearrangements that are reversed with each cycle. These results point to a microscopic view of mechanical properties under cyclic deformation.

Using high-speed video, we have studied air bubbles detaching from an underwater nozzle. As a bubble distorts, it forms a thin neck which develops a singular shape as it pinches off. As in other singularities, the minimum neck radius scales with the time until breakup. However, because the air-water interfacial tension does not drive breakup, even small initial cylindrical asymmetries are preserved throughout the collapse. This novel, non-universal singularity retains a memory of the nozzle shape, size and tilt angle. In the last stages, the air appears to tear instead of pinch.PACS numbers: 47.55.db, 47.55.df, 02.40.Xx The delightful tingling felt when drinking carbonated beverages, the glee of children blowing bubbles in a bathtub, and the importance of deep underwater fissures venting gasses into the oceans hint at the richness and significance of bubble formation in determining the texture and composition of our world. However, the process by which a bubble is formed is still full of surprises. A drop or bubble breaks up by forming a neck that thins to atomic dimensions, a process described as an approach towards a singularity where physical quantities such as stress or pressure grow infinitely large. Singularities often organize the overall dynamical evolution of nonlinear systems. Each symmetry in nature implies an underlying conservation law, so that the symmetries of the singularity associated with pinch-off naturally have important consequences for its dynamics. It was previously believed [1,2,3,4,5,6,7,8,9,10,11,12] that the pinching neck of any drop or bubble would become cylindrically (i.e. azimuthally) symmetric in the course of pinch-off. Recently, pinching necks of air in water were observed to lose cylindrical symmetry in the course of detachment [13,14].Here we show that this loss of symmetry is caused by a new form of memory in singular dynamics: even a small asymmetry in the initial conditions is preserved throughout bubble detachment. This novel singularity retains a memory of the nozzle shape, size and tilt angle. The asymmetry can be made so great that the air appears to tear. This symmetry breaking may be important in numerous applications [15,16,17], and for understanding other physical processes which are modeled as the formation of a singularity, such as star or black hole formation [18] and supernova explosions [19]. Thus our experimental observation of the breakdown of cylindrical symmetry in the air bubble demonstrates a new view of dynamical singularities that may be relevant even on a celestial scale.Singularities govern the dynamics in many familiar break-up events, such as the dispersal of oil drops into * Electronic address: nkeim@uchicago.edu vinegar during the making of a salad dressing, or the dripping of water from a leaky faucet. For many fluid pairs -for example, one viscous fluid breaking in a surrounding fluid of high viscosity [7,8,12] -the shape and dynamics of the pinching neck depend solely on the fluid parameters, as the breakup forgets its initial conditions on ...

A system with multiple transient memories can remember a set of inputs but subsequently forgets almost all of them, even as they are continually applied. If noise is added, the system can store all memories indefinitely. The phenomenon has recently been predicted for cyclically sheared nonBrownian suspensions. Here we present experiments on such suspensions, finding behavior consistent with multiple transient memories and showing how memories can be stabilized by noise.PACS numbers: 05.65.+b, 82.70.Kj A physical system has memory if it is endowed with the basic operations of imprinting, retrieval, and erasure. Common examples are mechanical marking or the flipping of magnetic domains. More exotic examples include return-point memory [1,2] and aging and rejuvenation in glasses [3,4]. These systems all support the intuition that (i) the more times an input is presented the stronger the memory becomes, and (ii) random noise is detrimental to memory retention. However, both attributes are violated by multiple transient memories, which have been seen in traveling charge-density waves [5,6] and predicted for sheared non-Brownian suspensions [7,8]. The experiments reported here on sheared suspensions demonstrate that noise can stabilize this form of memory retention.Keim and Nagel [7] described how multiple transient memories could occur in a simplified model of a suspension under cyclic shear: When sheared repeatedly between strain amplitudes γ = 0 and γ = γ 1 , a suspension can organize into a reversible steady state, thereby encoding a memory of γ 1 . The memory appears as a sudden drop in reversibility as the strain amplitude is swept past γ 1 . Multiple memories can be formed if several amplitudes, γ 1 < γ 2 < ... < γ n , are repeatedly applied. However, once the suspension relaxes to a state that is completely reversible up to amplitude γ n , it is also reversible for all γ < γ n ; thus the memories of all the smaller training amplitudes are effectively erased. The presence of noise was predicted to prevent the system from reaching a fully reversible state so that other memories could be retained.For multiple transient memories in charge-density waves, the role of noise was only demonstrated in a simulation [6]; in experiments [5] the ambient noise could not be varied and was assumed to be strong enough so that the system could remember all inputs. In the present paper, we cyclically shear neutrally buoyant, non-Brownian suspensions at low Reynolds number. By varying the noise, we demonstrate explicitly that noise is required to retain a memory of all input strain amplitudes at long times. This provides a concrete example of the emergence of plasticity in memory.Experiment.-In the experiment, a viscous suspension is cyclically sheared in a 6.3 mm gap between two cylinders in a circular Couette geometry (with an inner cylinder radius of 36.6 mm). The suspension is composed of PMMA spheres (Cospheric, LLC) in a mixture of Triton X-100, water, and zinc chloride (dynamic viscosity µ = 4,300 mPa s) that is index a...

The swimming behaviour of microorganisms can be strongly influenced by the rheology of their fluid environment. In this manuscript, we experimentally investigate the effects of shear-thinning viscosity on the swimming behaviour of an undulatory swimmer, the nematode Caenorhabditis elegans. Tracking methods are used to measure the swimmer's kinematic data (including propulsion speed) and velocity fields. We find that shear-thinning viscosity modifies the velocity fields produced by the swimming nematode but does not modify the nematode's speed and beating kinematics. Velocimetry data show significant enhancement in local vorticity and circulation, and an increase in fluid velocity near the nematode's tail, compared to Newtonian fluids of similar effective viscosity. These findings are compared to recent theoretical and numerical results. * parratia@seas.upenn.edu arXiv:1407.5854v2 [physics.flu-dyn]