Hydrodynamics of soft active matter

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.

Axially Loaded Timoshenko Rotors From A Prestressed Continuum Approach

We consider an axially loaded Timoshenko rotor rotating at a constant speed and derive its governing equations from a continuum viewpoint. The primary aim of this paper is to understand the source and role of gyroscopic terms, when the rotor is viewed not as a Timoshenko beam but as a genuine 3D continuum. We offer the primary insight that macroscopically observed gyroscopic terms may also, quite equivalently, be viewed as external manifestations of internally existing spin-induced prestresses at the continuum level. To demonstrate this idea with an analytical example (the Timoshenko rotor), we have studied the reliable equations of Choi et al. (Journal of Vibration and Acoustics, 114, 1992, 249-259). Using a straightforward application of our insight in the framework of nonlinear elasticity, we obtain equations that exactly match Choi et al. for the case with no axial load. For the case of axial preload, our straightforward formulation leads to a slightly different set of equations that have negligible numerical consequence for solid rotors. However, we offer a macroscopic, intuitive, justification for modifying our formulation so as to obtain the exact equations of Choi et al. with the axial load included.

Ultrafast Solvation Dynamics of an Ion in the gamma-Cyclodextrin Cavity: The Role of Restricted Environment

A detailed study of the solvation dynamics of a charged coumarin dye molecule in gamma-cyclodextrin/water has been carried out by using two different theoretical approaches. The first approach is based on a multishell continuum model (MSCM). This model predicts the time scales of the dynamics rather well, provided an accurate description of the frequency-dependent dielectric function is supplied. The reason for this rather surprising agreement is 2-fold. First, there is a cancellation of errors, second, the two-zone model mimics the heterogeneous microenvironment surrounding the ion rather well. The second approach is based on the molecular hydrodynamics theory (MI-IT). In this molecular approach, the solvation dynamics has been studied by restricting the translational motion of the solvent molecules enclosed within the cavity. The results from the molecular theory are also in good agreement with the experimental results. Our study indicates that, in the present case, the restricted environment affects only the long time decay of the solvation time correlation function. The short time dynamics is still governed by the librational (and/or vibrational) modes present in bulk water.

Hydrodynamics from the D1-brane

We study the hydrodynamic properties of strongly coupled SU(N) Yang-Mills theory of the D1-brane at finite temperature in the framework of gauge/gravity duality. The only non-trivial viscous transport coefficient in 1+1 dimensions is the bulk viscosity. We evaluate the bulk viscosity by isolating the quasi-normal mode corresponding to the sound channel for the gravitational background of the D1-brane. We find that the ratio of the bulk viscosity to the entropy density to be 1/4 pi. This ratio continues to be 1/4 pi also in the regime when the D1-brane Yang-Mills theory is dual to the gravitational background of the fundamental string. Our analysis shows that this ratio is equal to 1/4 pi for a class of gravitational backgrounds dual to field theories in 1+1 dimensions obtained by considering D1-branes at cones over Sasaki-Einstein 7-manifolds.

Continuum percolation with discs having a distribution of radii

It is shown that for continuum percolation with overlapping discs having a distribution of radii, the net areal density of discs at percolation threshold depends non-trivially on the distribution, and is not bounded by any finite constant. Results of a Monte Carlo simulation supporting the argument are presented.

The jump in vorticity across a shock wave in relativistic hydrodynamics

Using the singular surface theory, an expression for the jump in vorticity across a shock wave of arbitrary shape propagating in a uniform, perfect fluid occupying the space-time of special relativity, has been derived. It has been shown that the jump in vorticity across a shock of given strength and curvature depends only on the velocity of the medium ahead of the shock.

Review of continuum, finite element and hybrid techniques in the analysis of stress concentrations in structures

When a uniform flow of any nature is interrupted, the readjustment of the flow results in concentrations and rare-factions, so that the peak value of the flow parameter will be higher than that which an elementary computation would suggest. When stress flow in a structure is interrupted, there are stress concentrations. These are generally localized and often large, in relation to the values indicated by simple equilibrium calculations. With the advent of the industrial revolution, dynamic and repeated loading of materials had become commonplace in engine parts and fast moving vehicles of locomotion. This led to serious fatigue failures arising from stress concentrations. Also, many metal forming processes, fabrication techniques and weak-link type safety systems benefit substantially from the intelligent use or avoidance, as appropriate, of stress concentrations. As a result, in the last 80 years, the study and and evaluation of stress concentrations has been a primary objective in the study of solid mechanics. Exact mathematical analysis of stress concentrations in finite bodies presents considerable difficulty for all but a few problems of infinite fields, concentric annuli and the like, treated under the presumption of small deformation, linear elasticity. A whole series of techniques have been developed to deal with different classes of shapes and domains, causes and sources of concentration, material behaviour, phenomenological formulation, etc. These include real and complex functions, conformal mapping, transform techniques, integral equations, finite differences and relaxation, and, more recently, the finite element methods. With the advent of large high speed computers, development of finite element concepts and a good understanding of functional analysis, it is now, in principle, possible to obtain with economy satisfactory solutions to a whole range of concentration problems by intelligently combining theory and computer application. An example is the hybridization of continuum concepts with computer based finite element formulations. This new situation also makes possible a more direct approach to the problem of design which is the primary purpose of most engineering analyses. The trend would appear to be clear: the computer will shape the theory, analysis and design.

Starburst in the ultraluminous galaxy Arp 220: Constraints from observations of radio recombination lines and continuum

We present observations of radio recombination lines (RRL) from the starburst galaxy Arp 220 at 8.1 GHz (H92 alpha) and 1.4 GHz (H167 alpha and H165 alpha) and at 84 GHz (H42 alpha), 96 GHz (H40 alpha) and 207 GHz (H31 alpha) using the Very Large Array and the IRAM 30 m telescope, respectively. RRLs were detected at all the frequencies except 1.4 GHz, where a sensitive upper limit was obtained. We also present continuum flux measurements at these frequencies as well as at 327 MHz made with the VLA. The continuum spectrum, which has a spectral index alpha similar to -0.6 (S-nu proportional to nu(alpha)) between 5 and 10 GHz, shows a break near 1.5 GHz, a prominent turnover below 500 MHz, and a flatter spectral index above 50 GHz. We show that a model with three components of ionized gas with different densities and area covering factors can consistently explain both RRL and continuum data. The total mass of ionized gas in the three components is 3.2 x 10(7) M., requiring 3 x 10(5) O5 stars with a total Lyman continuum production rate N-Lyc similar to 1.3 x 10(55) photons s(-1). The ratio of the expected to observed Br alpha and Br gamma fluxes implies a dust extinction A(V) similar to 45 mag. The derived Lyman continuum photon production rate implies a continuous star formation rate (SFR) averaged over the lifetime of OB stars of similar to 240 M yr(-1). The Lyman continuum photon Production rate of similar to 3% associated with the high-density H II regions implies a similar SFR at recent epochs (t < 10(5) yr). An alternative model of high-density gas, which cannot be excluded on the basis of the available data, predicts 10 times higher SFR at recent epochs. If confirmed, this model implies that star formation in Arp 220 consists of multiple starbursts of very high SFR (few times 10(3) M. yr(-1)) and short duration (similar to 10(5) yr). The similarity of IR excess, L-IR/L-Ly alpha similar to 24, in Arp 220 to values observed in starburst galaxies shows that most of the high luminosity of Arp 220 is due to the ongoing starburst rather than to a hidden active galactic nucleus (AGN). A comparison of the IR excesses in Arp 220, the Galaxy, and M33 indicates that the starburst in Arp 220 has an initial mass function that is similar to that in normal galaxies and has a duration longer than 107 yr. If there was no infall of gas during this period, then the star formation efficiency (SFE) in Arp 220 is similar to 50%. The high SFR and SFE in Arp 220 is consistent with their known dependences on mass and density of gas in star-forming regions of normal galaxies.

Charge Density Analysis of Crystals of Nicotinamide with Salicylic Acid and Oxalic Acid: An Insight into the Salt to Cocrystal Continuum

Charge density analysis from both experimental and theoretical points of view on two molecular complexes: one is formed between nicotinamide and salicylic acid, and the other formed between nicotinamide and oxalic acid brings out the quantitative topological features to distinguish a cocrystal from a salt.

On the generalized continuum model of dipolar solvation dynamics

The continuum model of dipolar solvation dynamics is reviewed. The effects of non-spherical molecular shapes, of non-Debye dielectric relaxation of the polar solvent and of dielectric inhomogeneity of the solvent around the solute dipole are investigated. Several new theoretical results are presented. It is found that our generalized continuum model, which takes into account the dielectric inhomogeneity of the surrounding solvent, provides a description of solvation dynamics consistent with recent experimental results.

Analysis of continuum using boundary compatibility conditions of integrated force method

Static and vibration problems of an indeterminate continuum are traditionally analyzed by the stiffness method. The force method is more or less non-existent for such problems. This situation is primarily due to the incomplete state of development of the compatibility conditions which are essential for the analysis of indeterminate structures by the flexibility method. The understanding of the Compatibility Conditions (CC) has been substantially augmented. Based on the understanding of CC, a novel formulation termed the Integrated Force Method (IFM) has been established. In this paper IFM has been extended for the static and vibration analyses of a continuum. The IFM analysis is illustrated taking three examples: 1. (1) rectangular plate in flexure 2. (2) analysis of a cantilevered dam 3. (3) free vibration analysis of a beam. From the examples solved it is observed that the force response of an indeterminate continuum with mixed boundary conditions can be generated by IFM without any reference to displacements in the field or on the boundary. Displacements if required can be calculated by back substitution.

Hydrodynamics of the Renn-Lubensky twist grain boundary phase, and the decoupled lamellar phase

The long-wavelength hydrodynamics of the Renn-Lubensky twist grain boundary phase with grain boundary angle 2pialpha, alpha irrational, is studied. We find three propagating sound modes, with two of the three sound speeds vanishing for propagation orthogonal to the grains, and one vanishing for propagation parallel to the grains as well. In addition, we find that the viscosities eta1, eta2, eta4, and eta5 diverge like 1/Absolute value of omega as frequency omega --> 0, with the divergent parts DELTAeta(i) satisfying DELTAeta1DELTAeta4=(DELTAeta5)2, exactly. Our results should also apply to the predicted decoupled lamellar phase.

Molecular expression for dielectric friction on a rotating dipole: Reduction to the continuum theory

Recently we presented a microscopic expression for dielectric friction on a rotating dipole. This expression has a rather curious structure, involving the contributions of the transverse polarization modes of the solvent and also of the molecular length scale processes. It is shown here that under proper limiting conditions, this expression reduces exactly to the classical continuum model expression of Nee and Zwanzig [J. Chem. Phys. 52, 6353 (1970)]. The derivation requires the use of the asymptotic form of the orientation‐dependent total pair correlation function, the neglect of the contributions of translational modes of the solvent, and also the use of the limit that the size of the solvent molecules goes to zero. Thus, the derivation can be important in understanding the validity of the continuum model and can also help in explaining the results of a recent computer simulation study of dielectric relaxation in a Brownian dipolar lattice.

Nonlinear hydrodynamics of a hard-sphere fluid near the glass transition

We conduct a numerical study of the dynamic behavior of a dense hard-sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free-energy functional of the Ramakrishnan-Yussouff form. We find that the system exhibits glassy behavior as evidenced through a stretched exponential decay and a two-stage relaxation of the density correlation function. The characteristic times grow with increasing density according to the Vogel-Fulcher law. The wave-number dependence of the kinetics is extensively explored. The connection of our results with experiment, mode-coupling theory, and molecular-dynamics results is discussed.

Hydrodynamics of R-charged D1-branes

We study the hydrodynamic properties of strongly coupled SU(N) Yang-Mills theory of the D1-brane at finite temperature and at a non-zero density of R-charge in the framework of gauge/gravity duality. The gravity dual description involves a charged black hole solution of an Einstein-Maxwell-dilaton system in 3 dimensions which is obtained by a consistent truncation of the spinning D1-brane in 10 dimensions. We evaluate thermal and electrical conductivity as well as the bulk viscosity as a function of the chemical potential conjugate to the R-charges of the D1-brane. We show that the ratio of bulk viscosity to entropy density is independent of the chemical potential and is equal to 1/4 pi. The thermal conductivity and bulk viscosity obey a relationship similar to the Wiedemann-Franz law. We show that at the boundary of thermodynamic stability, the charge diffusion mode becomes unstable and the transport coefficients exhibit critical behaviour. Our method for evaluating the transport coefficients relies on expressing the second order differential equations in terms of a first order equation which dictates the radial evolution of the transport coefficient. The radial evolution equations can be solved exactly for the transport coefficients of our interest. We observe that transport coefficients of the D1-brane theory are related to that of the M2-brane by an overall proportionality constant which sets the dimensions.