In this review, we introduce granular materials as a condensed matter system and briefly discuss their general properties. We then focus on particle segregation in rapid, dense granular flows, a phenomenon that occurs more readily in granular materials than in other condensed matter systems. Our primary emphasis is on the development of continuum models to describe segregation in these systems. Over the years, numerous approaches have been proposed, each offering different perspectives on how to construct such models. Rather than providing an exhaustive review of any single approach, we compare and contrast various modeling strategies, highlighting their commonalities and respective advantages. By doing so, we aim to establish a clearer connection between different approaches, facilitating closer comparisons and potential synergies between them. We believe that bridging these approaches is essential for advancing our understanding and improving predictive capabilities in granular segregation modeling in the future.
Soft and active condensed matter represent a class of fascinating materials that we encounter in our everyday lives -- and constitute life itself. Control signals interact with the dynamics of these systems, and this influence is formalized in control theory and optimal control. Recent advances have employed various control-theoretical methods to design desired dynamics, properties, and functionality. Here we provide an introduction to optimal control aimed at physicists working with soft and active matter. We describe two main categories of control, feedforward control and feedback control, and their corresponding optimal control methods. We emphasize their parallels to Lagrangian and Hamiltonian mechanics, and provide a worked example problem. Finally, we review recent studies of control in soft, active, and related systems. Applying control theory to soft, active, and living systems will lead to an improved understanding of the signal processing, information flows, and actuation that underlie the physics of life.
The realization of the fractional quantum anomalous Hall effect (FQAHE) in a zero-field fractional Chern insulator is a new advancement in condensed matter physics, resulting from the interplay among strong correlations, topology, and spontaneous time-reversal symmetry breaking in lattice systems. In this review, we highlight the experimental and theoretical progress toward achieving FQAHE in two material platforms: twisted bilayer MoTe 2 and rhombohedral-stacked multilayer graphene. These systems host narrow topological bands with nontrivial Chern numbers, enabling interaction-driven fractionalized states analogous to the fractional quantum Hall effect, but without external magnetic fields. We discuss how spontaneous ferromagnetism, moiré lattice reconstruction, and band topological effects underpin the emergence of FQAHE in twisted MoTe 2 . We describe experimental discoveries of zero-field fractional Chern insulators in both transport and optical experiments, as well as signatures of composite Fermi liquids and higher-energy Chern band, which may shed light on engineering nonabelian states. In rhombohedral graphene/hexagonal boron nitride moiré superlattices, we review the recent observations of fractionally quantized Hall resistance, connections between FQAHE and extended quantum anomalous Hall phases, and the coexistence of superconductivity and FQAHE. These discoveries not only deepen our understanding of strongly correlated topological matter but also open new frontiers for exploring nonabelian anyons, fault-tolerant quantum computation, and topological opto-spintronics free of magnetic fields.
The discovery of ferroic orders in two-dimensional (2D) van der Waals (vdW) materials has introduced new functionalities to the 2D materials family, potentially revolutionizing next-generation nanoelectronics and spintronics. We provide a concise review of recent advances in 2D ferroics, with a focus on their experimental observations, the unique properties emerging from reduced dimensionality, and promising applications. We conclude by discussing key challenges that remain and offering our outlook on future research directions in this rapidly evolving field.
Understanding how cells coordinate their behaviors to produce large-scale patterns and functions is central to deciphering biological processes ranging from tissue development and regeneration to cancer progression and morphogenesis. Despite advances in imaging and mechanical characterization, the role of physical forces in collective cell dynamics remains incompletely understood. Physics-based models are essential for complementing experimental data, offering access to high-resolution spatiotemporal fields, and enabling mechanistic insights into complex multicellular systems. This review focuses on dense, soft tissues, in which the mechanical deformation of one cell drives reorganization of its neighbors, giving rise to emergent behaviors such as orientational order and long-range force transmission. The multiphase-field model provides a powerful and versatile framework to investigate such systems, bridging biological phenomena and the nonequilibrium physics of active matter. We discuss the theoretical foundations of the model and its applications to a range of biological contexts, including cell migration, heterogeneous populations, confined geometries, and metastasis. We also emphasize the integration of simulations with experimental data, highlighting how this approach is reshaping our understanding of tissue mechanics, collective order, and force transmission. Finally, we outline current trends and future challenges in applying multiphase-field models to biology and soft matter physics.
Ground states of materials with orientational order ranging from solid ferromagnets and ferroelectrics to liquid crystals often contain spatially varying vector-like order parameter caused by inner factors such as the shape of building units or by the geometry of confinement. This review presents examples of how the shapes, chirality, and polarity of molecules and spatial confinement induce deformed equilibrium and polydomain states with parity breaking, splay, bend, and twist-bend deformations of the order parameter in paraelectric and ferroelectric nematic liquid crystals. Parity breaking results either from chirality of the constituent molecules, as a replacement of energetically costly splay and bend in paraelectric nematics, or in response to depolarization field in the ferroelectric nematic. Both paraelectric and ferroelectric nematics exhibit a splay cancellation effect, in which the elastic and electrostatic energies of splay along one direction are reduced by an additional splay along orthogonal directions.
Biological tissue rheology investigates the mechanical behavior of tissues, emphasizing their viscoelastic and plastic properties that enable both solid-like elasticity and fluid-like viscosity under mechanical stress. These mechanical characteristics are pivotal in various physiological processes, such as embryonic development, tissue remodeling, wound healing, and pathological conditions including cancer metastasis. The mechanical responses of tissues, shaped by cellular forces and extracellular matrix dynamics, are crucial for maintaining tissue integrity and functionality. Rheological behaviors such as viscoelasticity, plasticity, and active mechanical responses underlie critical biological functions, enabling tissues to adapt structurally and functionally to internal and external stimuli. Recent theoretical and experimental advances have illuminated the complex interplay among cellular mechanics, biochemical signaling, and tissue-level forces, highlighting their roles in governing tissue morphogenesis, repair, and disease progression. This review synthesizes current knowledge, identifies key challenges, and discusses future directions for research in biological tissue rheology.
Active wetting extends classical wetting physics to living systems, in which cells and tissues spread by generating internal forces rather than relying solely on passive interfacial tensions. Unlike passive systems, which evolve toward thermodynamic and mechanical equilibrium by minimizing free energy, active systems remain far from equilibrium due to continuous energy input and dissipation. Their dynamics are sustained, adaptive, and responsive to chemical and mechanical cues in ways that depart fundamentally from passive behavior. In addition, active systems lack a unified energetic or variational principle to describe their evolution. What insights can be drawn from passive models, and how these models might be generalized to account for activity, remain open questions. Studying active wetting may thus reveal new principles of nonequilibrium dynamics at soft and living interfaces, and offer deeper understanding of key biological processes such as wound healing, cancer invasion, and biofilm growth.
Polar active matter—including animal herds, aggregates of motile cells, and active colloids—often forms coordinated migration patterns, such as flocking. This orderly motion can be disrupted by full-integer topological defects representing localized disturbances in which directional alignment is lost. Such polar defects can serve as key organizing centers across scales, sustaining collective behavior such as swirling motion and other large-scale coherent states. Although significant progress has been made in understanding active matter principles in recent years, a quantitative understanding of how topological defects influence active polar matter is still needed. We present a brief overview of recent experimental observations in synthetic active colloids and various biological systems. We describe how polar defects mediate dynamical transitions and contribute to the spontaneous emergence of large-scale coherent states. We also discuss theoretical advances in the physical modeling of coupled processes involving polar defects and collective behavior in active polar matter.
Ultracold Bose gases of highly magnetic atoms exhibit unique interaction properties that lead to striking many-body behaviors, both at and beyond the mean field. A decade ago, a universal stabilization mechanism driven by quantum fluctuations was discovered in these gases. This mechanism prevents the systems from collapsing and instead allows exotic states of matter to arise, including ultradilute quantum droplets, crystallized quantum states, and especially supersolids. After introducing key features of dipolar quantum Bose gases—including their interactions, ground states, and excitations in a mean-field framework, as well as the onset of quantum-fluctuation stabilization—we review the progress made in understanding the emergence and intriguing properties of these quantum stabilized states. Both theory and experiments are discussed.
Disordered systems subject to a fluctuating environment can self-organize into a complex history-dependent response, retaining a memory of the driving. In sheared amorphous solids, self-organization is established by the emergence of a persistent system of mechanical instabilities that can repeatedly be triggered by the driving, leading to a state of high mechanical reversibility. As a result of self-organization, the response of the system becomes correlated with the dynamics of its environment, which can be viewed as a sensing mechanism of the system's environment. Such phenomena emerge across a wide variety of soft matter systems, suggesting that they are generic and hence may depend very little on the underlying specifics. We review self-organization in driven amorphous solids, concluding with a discussion of what self-organization in driven disordered systems can teach us about how simple organisms sense and adapt to their changing environments.
This article is the result of a transcribed recording of an interview that Ram Seshadri [Materials and Chemistry, University of California, Santa Barbara (UCSB)] conducted with Fyl Pincus who recently retired from UCSB (Physics and Materials). Its focus is an autobiographical account of Fyl's academic career and includes a personal view of the early days of soft condensed matter as a subdiscipline of physics.
Feedback control is essential to the performance of dynamical systems, helping to drive nonequilibrium systems from one state to another. In this review, we discuss feedback control applied to living and synthetic active matter—systems that are constantly dynamical and out of equilibrium. We review the experimental and theoretical work in controlling the trajectory and distribution of active matter, from single particles to collective populations. Modern advances in microscopy and numerical computation have enabled data-rich studies of active systems, aided by data-driven approaches to model, forecast, and control the complex and chaotic behaviors of active matter. We describe the basic mathematical structure of active Brownian particles, with a focus on observability and time delay embedding to control particle motion using density data alone. Finally, we comment on the future outlook of controlling complex systems with multibody interparticle and hydrodynamic interactions.
Understanding superconductivity in its myriad forms arising in numerous different crystal architectures is one of the major quests of modern condensed matter physics. One promising avenue to gain local information about novel superconductors is the use of local probes to measure properties inside the unit cell. The application of muon spin spectroscopy to the study of various superconducting materials is reviewed. These experiments can be carried out as a function of temperature, magnetic field, and pressure and even in thin-film samples. They provide information about proximal magnetic phases and the nature of the superconducting state, as well as giving intriguing evidence of time-reversal symmetry breaking. To properly interpret the experimental results, it is necessary to have reliable information about the site of the implanted muon, as well as its stability. This can now be provided using density functional theory techniques.
Turbulent motion of fluids is often thought of as a grand problem, but what exactly is this “turbulence problem”? Because it has often been proclaimed as very difficult and unsolved, when can we claim that it is solved? How does this situation in turbulence compare with other complex problems in physical sciences? Addressing these questions is not trivial because everyone has their favorite idea of what is required of the “solution.” The answers range from being able to calculate the pressure drop in turbulent pipe flow to being able to calculate anomalous scaling exponents to answering the regularity problem of the Navier–Stokes equations. Taking an absolute position on the basis of any of these, or other similar examples, is incomplete at best and potentially erroneous at worst. We believe that it is beneficial to have an open discussion of this topic for the advancement of the research agenda in turbulence. This article is an attempt to address the question of what constitutes the turbulence problem, its place in the scientific enterprise as a whole, and how and when one may declare it as solved.
A rich variety of amorphous solids are found in nature and technology, including ones formed via the vulcanization of long, flexible molecules. A special class – those featuring a wide gap between the long timescales over which constraints in them release and the much shorter timescales over which their unconstrained freedoms relax – exhibit states of thermodynamic equilibrium and are thus amenable to the framework of equilibrium statistical physics. The approach reviewed here is the least specific – and thus the most general – approach to the statistical mechanics of equilibrium amorphous solid-formers: statistical field theory. An overview is given of the key elements and results of this theory. The field of the theory is constructed to detect and diagnose the amorphous solid state. Its form turns out to be unusual, in ways that are essential for its application, so it is examined in detail, as is the form of the field theory controlling the field. What this theory can predict for the equilibrium properties of amorphous solids is then discussed, including: the transition to the amorphous solid state and the heterogeneity of the resulting solid; the impact of fluctuations on the transition and connections with percolation theory; the pattern of symmetry-breaking and the nature of the resulting elasticity; and field correlations and the information they provide. Emphasis is placed on the idea, peculiar to amorphous solids, that their equilibrium states are naturally characterized in terms of distributions that capture the intrinsic spatial heterogeneity of the thermal motions of their constituents. The theory's field has an internal structure that subtly encodes this information, via the wave-vector dependencies of the average field and its correlations. Reflections are made on the applicability of theses ideas and results to a range of amorphous solids and related systems.
Mixtures of nematic liquid crystals and isotropic fluids display a diverse range of phase behaviors, arising from the coupling between orientational order and concentration fluctuations. In this review, we introduce a simplified mathematical framework that integrates the Landau-de Gennes free energy for nematic ordering with the Cahn-Hilliard free energy for phase separation. We derive the corresponding governing equations and analyze the stability of uniform phases, along with the resulting interfacial phenomena. The review concludes with a brief discussion highlighting key differences in phase separation between mixtures of isotropic fluids with passive and active nematics.
I review some recent results on understanding the physics of metals in an exact non-perturbative way through the powerful field-theoretic concepts of emergent symmetries and 't Hooft anomalies. A 't Hooft anomaly is a discrete topological property that quantum field theories with global symmetries can have. I explain how many of the properties of metals can in fact be viewed as direct consequences of the anomaly. This allows a structural understanding of metals, including non-Fermi liquids, to be obtained even in the absence of any exact solution for the strongly coupled dynamics. I then outline the main limitations and outstanding questions.
Nearly thirty years after its inception, the field of DNA-programmed colloidal self-assembly has begun to realize its initial promise. In this review, we summarize recent developments in designing effective interactions and understanding the dynamic self-assembly pathways of DNA-coated nanoparticles and microparticles, as well as how these advances have propelled tremendous progress in crystal engineering. We also highlight exciting new directions showing that new classes of subunits combining nanoparticles with DNA origami can be used to engineer novel multicomponent assemblies, including structures with self-limiting, finite sizes. We conclude by providing an outlook on how recent theoretical advances focusing on the kinetics of self-assembly could usher in new materials-design opportunities, like the possibility of retrieving multiple distinct target structures from a single suspension or accessing new classes of materials that are stabilized by energy dissipation, mimicking self-assembly in living systems.
The dynamic charge susceptibility, $\chi(q,\omega)$, is a fundamental observable of all materials, in one, two, and three dimensions, quantifying the collective charge modes, the ability of a material to screen charge, as well as its electronic compressibility. Here, we review the current state of efforts to measure this quantity using inelastic electron scattering, which historically has been called electron energy-loss spectroscopy (EELS). We focus on comparison between transmission (T-EELS) and reflection (R-EELS) geometries as applied to a selection of 3D conductors. While a great deal is understood about simple metals, measurements of more strongly interacting and strange metals are currently contradictory, with different groups obtaining fundamentally conflicting results, emphasizing the importance of improved EELS measurements. Further, current opportunities for improvement in EELS techniques are vast, with the most promising future developments being in hemispherical and time-of-flight analyzers, as well as STEM instruments configured for high momentum resolution. We conclude that, despite more than half a century of work, EELS techniques are currently still in their infancy
