# Hyperuniformity

Aliases

This identifies the pattern and should be representative of the concept that it describes. The name should be a noun that should be easily usable within a sentence. We would like the pattern to be easily referenceable in conversation between practitioners.

Intent

Describes in a single concise sentence the meaning of the pattern.

Motivation

The most likely solution to a high-dimensional optimization problem is one where the parameters are with high entropy. High entropy is most likely configuration state of any dynamical system. The discovery of a configuration with sparsity or with disentanglement is less likely to happen. There are systems in physics that appear random but have hidden structure, the characteristic of these systems is called hyperuniformity.

If generalization is achieved through regularization (i.e. the introduction of constraints) then we can argue that the system will evolve towards a state that will conform to these constraints. Therefore despite evolving towards a high entropy state, the system will settle to some structure in the randomness.

Sketch

This section provides alternative descriptions of the pattern in the form of an illustration or alternative formal expression. By looking at the sketch a reader may quickly understand the essence of the pattern.

Discussion

This is the main section of the pattern that goes in greater detail to explain the pattern. We leverage a vocabulary that we describe in the theory section of this book. We donâ€™t go into intense detail into providing proofs but rather reference the sources of the proofs. How the motivation is addressed is expounded upon in this section. We also include additional questions that may be interesting topics for future research.

Known Uses

Here we review several projects or papers that have used this pattern.

Related Patterns In this section we describe in a diagram how this pattern is conceptually related to other patterns. The relationships may be as precise or may be fuzzy, so we provide further explanation into the nature of the relationship. We also describe other patterns may not be conceptually related but work well in combination with this pattern.

Relationship to Canonical Patterns

Relationship to other Patterns

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References

To aid in reading, we include sources that are referenced in the text in the pattern.

http://arxiv.org/pdf/0808.2196v1.pdf Jamming II: A phase diagram for jammed matter

http://arxiv.org/pdf/1506.01948v2.pdf Search for Hyperuniformity in Mechanically Stable Packings of Frictionless Disks Above Jamming

http://arxiv.org/pdf/1504.04638v2.pdf Emergent hyperuniformity in periodically-driven emulsions

Upon periodic driving confined emulsions undergo a first-order transition from a reversible to an irreversible dynamics. We evidence that this dynamical transition is accompanied by structural changes at all scales yielding macroscopic yet finite hyperuniform structures.

We show that as opposed to equilibrium systems the long-range nature of the hydrodynamic interactions are not required for the formation of hyperuniform patterns, thereby suggesting a robust relation between reversibility and hyperuniformity which should hold in a broad class of periodically driven materials.

Surprisingly, unlike in equilibrium systems, we show that long-range interactions are not necessary to yield extended hyperuniform structures. We therefore conjecture that hyperuniformity is intimately related to reversibility in periodically driven systems, and should therefore be achieved in a broad class of hard and soft condensed matter materials.