Generic Transient Memory Formation in Disordered Systems with Noise

Abstract

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...

Multiple Transient Memories in Experiments on Sheared Non-Brownian Suspensions

“…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 .…”

“…These have many of the properties of multiple transient memories [5][6][7][8]: (i) the suspension can learn multiple memories, (ii) the memory of the smaller input strain is erased even as that input is continually applied, and (iii) the memory of the smaller input value is stabilized by the presence of noise. Also, as in charge-density waves, the sheared suspensions remember the direction of the last applied deformation [13].…”

Precisely cyclic sand: Self-organization of periodically sheared frictional grains

“…The present system, with thousands of degrees of freedom, highly nonlinear and hysteretic equations of motion is a paradigm for chaotic behavior; therefore, it is surprising it exhibits a disordered absorbing state. The absorbing state dynamics found in nonBrownian suspensions at low Reynolds number are capable of encoding a rudimentary memory of the system's driving history (23), yet in these systems noise is required to retain memories beyond a single shear amplitude. Recent simulations found that dense amorphous solids can retain multiple memories in a similar fashion, but without the need for added noise (24).…”

Period proliferation in periodic states in cyclically sheared jammed solids

“…As the strain amplitude γ t increases beyond some value γ * t , particles can no longer avoid each other and the system undergoes a dynamical "absorbing state" transition from the absorbing phase to a phase in which the system continually visits new configurations. Models [3,[5][6][7][8] have linked this transition to variants of directed percolation [8][9][10], which represents a broad class of non-equilibrium phase transitions [1].…”