Theoretical study of time-dependent, ultrasound-induced acoustic streaming in microchannels

Based on first- and second-order perturbation theory, we present a numerical study of the temporal build-up and decay of unsteady acoustic fields and acoustic streaming flows actuated by vibrating walls in the transverse cross-sectional plane of a long straight microchannel under adiabatic conditions and assuming temperature-independent material parameters. The unsteady streaming flow is obtained by averaging the time-dependent velocity field over one oscillation period, and as time increases, it is shown to converge towards the well-known steady time-averaged solution calculated in the frequency domain. Scaling analysis reveals that the acoustic resonance builds up much faster than the acoustic streaming, implying that the radiation force may dominate over the drag force from streaming even for small particles. However, our numerical time-dependent analysis indicates that pulsed actuation does not reduce streaming significantly due to its slow decay. Our analysis also shows that for an acoustic resonance with a quality factor Q, the amplitude of the oscillating second-order velocity component is Q times larger than the usual second-order steady time-averaged velocity component. Consequently, the well-known criterion v << c for the validity of the perturbation expansion is replaced by the more restrictive criterion v << c/Q. Our numerical model is available in the supplemental material in the form of Comsol model files and Matlab scripts.Comment: 14 pages, Revtex, 8 eps figure

Tropical tree height and crown allometries for the Barro Colorado Nature Monument, Panama: a comparison of alternative hierarchical models incorporating interspecific variation in relation to life history traits

Tree allometric relationships are widely employed for estimating forest biomass and production and are basic building blocks of dynamic vegetation models. In tropical forests, allometric relationships are often modeled by fitting scale-invariant power functions to pooled data from multiple species, an approach that fails to capture changes in scaling during ontogeny and physical limits to maximum tree size and that ignores interspecific differences in allometry. Here, we analyzed allometric relationships of tree height (9884 individuals) and crown area (2425) with trunk diameter for 162 species from the Barro Colorado Nature Monument, Panama. We fit nonlinear, hierarchical models informed by species traits – wood density, mean sapling growth, or sapling mortality – and assessed the performance of three alternative functional forms: the scale-invariant power function and the saturating Weibull and generalized Michaelis–Menten (gMM) functions. The relationship of tree height with trunk diameter was best fit by a saturating gMM model in which variation in allometric parameters was related to interspecific differences in sapling growth rates, a measure of regeneration light demand. Light-demanding species attained taller heights at comparatively smaller diameters as juveniles and had shorter asymptotic heights at larger diameters as adults. The relationship of crown area with trunk diameter was best fit by a power function model incorporating a weak positive relationship between crown area and species-specific wood density. The use of saturating functional forms and the incorporation of functional traits in tree allometric models is a promising approach for improving estimates of forest biomass and productivity. Our results provide an improved basis for parameterizing tropical plant functional types in vegetation models.</p

Equilibrium Relativistic Mass Distribution for Indistinguishable Events

A manifestly covariant relativistic statistical mechanics of the system of $N$ indistinguishable events with motion in space-time parametrized by an invariant ``historical time'' $\tau$ is considered. The relativistic mass distribution for such a system is obtained from the equilibrium solution of the generalized relativistic Boltzmann equation by integration over angular and hyperbolic angular variables. All the characteristic averages are calculated. Expressions for the pressure and the density of events are found and the relativistic equation of state is obtained. The Galilean limit is considered; the theory is shown to pass over to the usual nonrelativistic statistical mechanics of indistinguishable particles.Comment: TAUP-2115-9

Random-phase Approximation Treatment Of Edge Magnetoplasmons: Edge-state Screening And Nonlocality

A random-phase approximation (RPA) treatment of edge magnetoplasmons (EMP) is presented for strong magnetic fields, low temperatures, and integer filling factors \nu. It is valid for negligible dissipation and lateral confining potentials smooth on the scale of the magnetic length \ell_{0} but sufficiently steep that the Landau-level (LL) flattening can be neglected. LL coupling, screening by edge states, and nonlocal contributions to the current density are taken into account. In addition to the fundamental mode with typical dispersion relation \omega\sim q_x \ln(q_{x}), fundamental modes with {\it acoustic} dispersion relation \omega\sim q_x are obtained for \nu>2. For \nu=1,2 a {\bf dipole} mode exists, with dispersion relation \omega\sim q_x^3, that is directly related to nonlocal responses.Comment: Text 12 pages in Latex/Revtex format, 4 Postscript figure

Topography and instability of monolayers near domain boundaries

We theoretically study the topography of a biphasic surfactant monolayer in the vicinity of domain boundaries. The differing elastic properties of the two phases generally lead to a nonflat topography of ``mesas'', where domains of one phase are elevated with respect to the other phase. The mesas are steep but low, having heights of up to 10 nm. As the monolayer is laterally compressed, the mesas develop overhangs and eventually become unstable at a surface tension of about K(dc)^2 (dc being the difference in spontaneous curvature and K a bending modulus). In addition, the boundary is found to undergo a topography-induced rippling instability upon compression, if its line tension is smaller than about K(dc). The effect of diffuse boundaries on these features and the topographic behavior near a critical point are also examined. We discuss the relevance of our findings to several experimental observations related to surfactant monolayers: (i) small topographic features recently found near domain boundaries; (ii) folding behavior observed in mixed phospholipid monolayers and model lung surfactants; (iii) roughening of domain boundaries seen under lateral compression; (iv) the absence of biphasic structures in tensionless surfactant films.Comment: 17 pages, 9 figures, using RevTeX and epsf, submitted to Phys Rev

Elastic turbulence in curvilinear flows of polymer solutions

Following our first report (A. Groisman and V. Steinberg, \sl Nature $\bf 405$, 53 (2000)) we present an extended account of experimental observations of elasticity induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of width of the region available for flow to radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high molecular weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. Those include: (i)randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales; (ii) significant increase in the rates of momentum and mass transfer (compared to those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms, and parameter dependence of the elastic turbulence are compared with those of the conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure

Mechanical Strength of 17 134 Model Proteins and Cysteine Slipknots

A new theoretical survey of proteins' resistance to constant speed stretching is performed for a set of 17 134 proteins as described by a structure-based model. The proteins selected have no gaps in their structure determination and consist of no more than 250 amino acids. Our previous studies have dealt with 7510 proteins of no more than 150 amino acids. The proteins are ranked according to the strength of the resistance. Most of the predicted top-strength proteins have not yet been studied experimentally. Architectures and folds which are likely to yield large forces are identified. New types of potent force clamps are discovered. They involve disulphide bridges and, in particular, cysteine slipknots. An effective energy parameter of the model is estimated by comparing the theoretical data on characteristic forces to the corresponding experimental values combined with an extrapolation of the theoretical data to the experimental pulling speeds. These studies provide guidance for future experiments on single molecule manipulation and should lead to selection of proteins for applications. A new class of proteins, involving cystein slipknots, is identified as one that is expected to lead to the strongest force clamps known. This class is characterized through molecular dynamics simulations.Comment: 40 pages, 13 PostScript figure

Dynamical mean-field theory of the small polaron

A dynamical mean-field theory of the small polaron problem is presented, which becomes exact in the limit of infinite dimensions. The ground state properties and the one-electron spectral function are obtained for a single electron interacting with Einstein phonons by a mapping of the lattice problem onto a polaronic impurity model. The one-electron propagator of the impurity model is calculated through a continued fraction expansion (CFE), both at zero and finite temperature, for any electron-phonon coupling and phonon energy. In contrast to the ground state properties such as the effective polaron mass, which have a smooth behaviour, spectral properties exhibit a sharp qualitative change at low enough phonon frequency: beyond a critical coupling, one energy gap and then more and more open in the density of states at low energy, while the high energy part of the spectrum is broad and can be explained by a strong coupling adiabatic approximation. As a consequence narrow and coherent low-energy subbands coexist with an incoherent featureless structure at high energy. The subbands denote the formation of quasiparticle polaron states. Also, divergencies of the self-energy may occur in the gaps. At finite temperature such effect triggers an important damping and broadening of the polaron subbands. On the other hand, in the large phonon frequency regime such a separation of energy scales does not exist and the spectrum has always a multipeaked structure.Comment: 21 Pages Latex, 19 PostScript figure

The Raychaudhuri equations: a brief review

We present a brief review on the Raychaudhuri equations. Beginning with a summary of the essential features of the original article by Raychaudhuri and subsequent work of numerous authors, we move on to a discussion of the equations in the context of alternate non--Riemannian spacetimes as well as other theories of gravity, with a special mention on the equations in spacetimes with torsion (Einstein--Cartan--Sciama--Kibble theory). Finally, we give an overview of some recent applications of these equations in General Relativity, Quantum Field Theory, String Theory and the theory of relativisitic membranes. We conclude with a summary and provide our own perspectives on directions of future research.Comment: 35 pages, two figures, to appear in the special issue of Pramana dedicated to the memory of A. K. Raychaudhur