Unified Hydrodynamic Theory for Crystals, Liquid Crystals, and Normal Fluids
TL;DR: In this paper, a unified hydrodynamic theory is presented that is appropriate for crystals; smectic, cholesteric, and nematic liquid crystals; glasses; and normal fluids.
Abstract: A unified hydrodynamic theory is presented that is appropriate for crystals; smectic, cholesteric, and nematic liquid crystals; glasses; and normal fluids. In the theory, the increased spatial degeneracy as the system progresses from crystalline and mesomorphic phases to the isotropic fluid phase is marked by successive reductions in the number of firstorder elastic constants and in the number of transport coefficients. Distinction between local lattice dilations and local mass changes, and recognition of processes like vacancy diffusion that this difference makes possible, are crucial for understanding the connection between theories in different phases. Formulas are derived that give the number of hydrodynamic modes and the frequencies, lifetimes, and intensities of these modes in all of the above systems. In the nematic and cholesteric phases, the results agree with some found previously. In more complex systems, they are new. An attempt is made to explain the differences between the present hydrodynamic theory and other phenomenological proposals.
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TL;DR: This review summarizes theoretical progress in the field of active matter, placing it in the context of recent experiments, and highlights the experimental relevance of various semimicroscopic derivations of the continuum theory for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular material.
Abstract: This review summarizes theoretical progress in the field of active matter, placing it in the context of recent experiments. This approach offers a unified framework for the mechanical and statistical properties of living matter: biofilaments and molecular motors in vitro or in vivo, collections of motile microorganisms, animal flocks, and chemical or mechanical imitations. A major goal of this review is to integrate several approaches proposed in the literature, from semimicroscopic to phenomenological. In particular, first considered are ``dry'' systems, defined as those where momentum is not conserved due to friction with a substrate or an embedding porous medium. The differences and similarities between two types of orientationally ordered states, the nematic and the polar, are clarified. Next, the active hydrodynamics of suspensions or ``wet'' systems is discussed and the relation with and difference from the dry case, as well as various large-scale instabilities of these nonequilibrium states of matter, are highlighted. Further highlighted are various large-scale instabilities of these nonequilibrium states of matter. Various semimicroscopic derivations of the continuum theory are discussed and connected, highlighting the unifying and generic nature of the continuum model. Throughout the review, the experimental relevance of these theories for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular material is discussed. Promising extensions toward greater realism in specific contexts from cell biology to animal behavior are suggested, and remarks are given on some exotic active-matter analogs. Last, the outlook for a quantitative understanding of active matter, through the interplay of detailed theory with controlled experiments on simplified systems, with living or artificial constituents, is summarized.
3,314 citations
Additional excerpts
...Such a division is unambiguous when there are collective excitations with relaxation rates!ðqÞ that vanish as the wave vector q goes to zero; these are the hydrodynamic modes of the systems (Martin, Parodi, and Pershan, 1972; Forster, 1975)....
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...The evolution of these fields is written in terms of a set of continuum or hydrodynamic equations that modify the well-known liquidcrystal hydrodynamics (Martin, Parodi, and Pershan, 1972; de Gennes and Prost, 1993) to include new nonequilibrium terms that arise from the activity....
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...Generalized hydrodynamic theories have been very successful in the description of many condensed matter systems, such as superfluids (Dzyaloshinskii and Volovick, 1980), liquid crystals (Martin, Parodi, and Pershan, 1972), polymers (Milner, 1993), as well as, of course, simple fluids....
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...This approach involves a systematic derivation of the hydrodynamic equations based on a generalized hydrodynamic approach close to equilibrium closely following the work of Martin, Parodi, and Pershan for nemato hydrodynamics (Martin, Parodi, and Pershan, 1972; de Gennes and Prost, 1993)....
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...…the hydrodynamic equations of active matter are then seen to be a consequence of off-diagonal Onsager coefficients and an imposed constant nonzero !!. Generalized hydrodynamic theories have been very successful in the description of complex and simple fluids (Martin, Parodi, and Pershan, 1972)....
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TL;DR: In this paper, a unified view of the many kinds of active matter is presented, encompassing not only living systems but inanimate analogs, including all living organisms and their motile constituents such as molecular motors.
Abstract: Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular motors. This article reviews recent progress in applying the principles of nonequilibrium statistical mechanics and hydrodynamics to form a systematic theory of the behavior of collections of active particles–active matter–with only minimal regard to microscopic details. A unified view of the many kinds of active matter is presented, encompassing not only living systems but inanimate analogs. Theory and experiment are discussed side by side.
1,546 citations
TL;DR: In this article, the physical properties of nematic, cholesteric, and smectic liquid crystals are discussed and a wide variety of phenomena in liquid crystals, including elastic distortions, disclinations, flow properties, fluctuations, light scattering, wave propagation, nuclear magnetic resonance, effects of magnetic and electric fields, electrohydrodynamics, and optical properties.
Abstract: This review discusses the physical properties of nematic, cholesteric, and smectic liquid crystals. Molecular theories of the liquid crystal phases are discussed and the molecular field theories of the phase transitions between the various liquid crystal phases are presented. The elastic theory and hydrodynamics of liquid crystals is developed. A wide variety of phenomena in liquid crystals, including elastic distortions, disclinations, flow properties, fluctuations, light scattering, wave propagation, nuclear magnetic resonance, effects of magnetic and electric fields, electrohydrodynamics, and optical properties, is discussed.
978 citations
TL;DR: In this article, the authors review the theoretical and experimental studies of flocking: the collective, coherent motion of large numbers of self-propelled "particles" (usually, but not always, living organisms).
839 citations
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TL;DR: Active gel physics as discussed by the authors is a field that has emerged in recent years to fill this gap and is underpinned by a theory that takes into account the transduction of chemical energy on the molecular scale.
Abstract: The mechanical behaviour of cells is largely controlled by a structure that is fundamentally out of thermodynamic equilibrium: a network of crosslinked filaments subjected to the action of energy-transducing molecular motors. The study of this kind of active system was absent from conventional physics and there was a need for both new theories and new experiments. The field that has emerged in recent years to fill this gap is underpinned by a theory that takes into account the transduction of chemical energy on the molecular scale. This formalism has advanced our understanding of living systems, but it has also had an impact on research in physics per se. Here, we describe this developing field, its relevance to biology, the novelty it conveys to other areas of physics and some of the challenges in store for the future of active gel physics. Equilibrium physics is ill-equipped to explain all of life’s subtleties, largely because living systems are out of equilibrium. Attempts to overcome this problem have given rise to a lively field of research—and some surprising biological findings.
611 citations
Cites background from "Unified Hydrodynamic Theory for Cry..."
...The reason for this surprising feature is contained in a subtle multicomponent version of active gels, inspired from polymer physics and in which the stresses due to the gel are kept as an independent variable18 (Box 1, equation (8))....
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