Breakup of double emulsions in constrictions

We report the controlled breakup of double emulsion droplets as they flow through an orifice of a tapered nozzle. The results are summarized in a phase diagram in terms of the droplet-to-orifice diameter ratio and the capillary number. We identify a flow regime where the inner aqueous phase is released. © 2011 The Royal Society of Chemistry.postprin

Symmetries and exact solutions of some integrable Haldane-Shastry like spin chains

By using a class of `anyon like' representations of permutation algebra, which pick up nontrivial phase factors while interchanging the spins of two lattice sites, we construct some integrable variants of $SU(M)$ Haldane-Shastry (HS) spin chain. Lax pairs and conserved quantities for these spin chains are also found and it is established that these models exhibit multi-parameter deformed or nonstandard variants of $Y(gl_M)$ Yangian symmetry. Moreover, by projecting the eigenstates of Dunkl operators in a suitable way, we derive a class of exact eigenfunctions for such HS like spin chain and subsequently conjecture that these exact eigenfunctions would lead to the highest weight states associated with a multi-parameter deformed or nonstandard variant of $Y(gl_M)$ Yangian algebra. By using this conjecture, and acting descendent operator on the highest weight states associated with a nonstandard $Y(gl_2)$ Yangian algebra, we are able to find out the complete set of eigenvalues and eigenfunctions for the related HS like spin-${1\over 2}$ chain. It turns out that some additional energy levels, which are forbidden due to a selection rule in the case of SU(2) HS model, interestingly appear in the spectrum of above mentioned HS like spin chain having nonstandard $Y(gl_2)$ Yangian symmetry.Comment: 35 pages, latex, no figures, minor type errors are corrected, version to appear in Nucl. Phys.

Early-time free-surface flow driven by a deforming boundary

AbstractWhen a solid boundary deforms rapidly into a quiescent liquid layer, a flow is induced that can lead to jet formation. An asymptotic analytical solution is presented for this flow, driven by a solid boundary deforming with dimensionless vertical velocity $V_{b}(x,t)={\it\epsilon}(1+\cos x)\,f(t)$, where the amplitude ${\it\epsilon}$ is small relative to the wavelength and the time dependence $f(t)$ approaches 0 for large $t$. Initially, the flow is directed outwards from the crest of the deformation and slows with the slowing of the boundary motion. A domain-perturbation method is used to reveal that, when the boundary stops moving, nonlinear interactions with the free surface leave a remnant momentum directed back towards the crest, and this momentum can be a precursor to jet formation. This scenario arises in a laser-induced printing technique in which an expanding blister imparts momentum into a liquid film to form a jet. The analysis provides insight into the physics underlying the interaction between the deforming boundary and free surface, in particular, the dependence of the remnant flow on the thickness of the liquid layer and the deformation amplitude and wavelength. Numerical simulations are used to show the range of validity of the analytical results, and the domain-perturbation solution is extended to an axisymmetric domain with a Gaussian boundary deformation to compare with previous numerical simulations of blister-actuated laser-induced forward transfer.The authors gratefully acknowledge financial support for this research from the Na- tional Science Foundation MRSEC program through the Princeton Center for Complex Materials (grant DMR-0819860).This is the accepted manuscript. The final published version is available from CUP at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9571518&fileId=S0022112015000749

Spin dependent extension of Calogero-Sutherland model through anyon like representations of permutation operators

We consider a $A_{N-1}$ type of spin dependent Calogero-Sutherland model, containing an arbitrary representation of the permutation operators on the combined internal space of all particles, and find that such a model can be solved as easily as its standard $su(M)$ invariant counterpart through the diagonalisation of Dunkl operators. A class of novel representations of the permutation operator $P_{ij}$, which pick up nontrivial phase factors along with interchanging the spins of $i$-th and $j$-th particles, are subsequently constructed. These `anyon like' representations interestingly lead to different variants of spin Calogero-Sutherland model with highly nonlocal interactions. We also explicitly derive some exact eigenfunctions as well as energy eigenvalues of these models and observe that the related degeneracy factors crucially depend on the choice of a few discrete parameters which characterise such anyon like representations.Comment: 25 pages, plain LaTex file, the results of sec.4 are presented in a more explicit way, to appear in Nucl. Phys.

Steric effects of ions in the charge-related wetting phenomena

Steric effects of ions on the charge-related wetting phenomena are studied. Along with a general treatment, three specific problems in two-dimensional system are considered: a droplet on an electrode, a droplet on a charged surface, and an electrowetting phenomenon on a dielectric. For computation of wetting tension, the electromechanical approach is adopted with the principle of mechanical force balance for each phase. The modified Poisson-Boltzmann equation, which was originally proposed by Bikerman [Philos. Mag. 33, 384 (1942)], is adopted for the analysis of the steric effects. It is found that the steric hindrance reduces significantly both the osmotic pressure and the electrical stress near the triple contact line. This reduction results in a considerable decrease in the wetting tension when the ratio of the capacitance per unit area of the electrical double layer to that of the dielectric layer is small.open111817sciescopu

All the Exact Solutions of Generalized Calogero-Sutherland Models

A collective field method is extended to obtain all the explicit solutions of the generalized Calogero-Sutherland models that are characterized by the roots of all the classical groups, including the solutions corresponding to spinor representations for $B_N$ and $D_N$ cases.Comment: Latex, 17 pages. Title and abstract slightly changed, plus minor correction

Multi-parameter deformed and nonstandard Y(glM)Y(gl_M) Yangian symmetry in integrable variants of Haldane-Shastry spin chain

By using `anyon like' representations of permutation algebra, which pick up nontrivial phase factors while interchanging the spins of two lattice sites, we construct some integrable variants of Haldane-Shastry (HS) spin chain. Lax equations for these spin chains allow us to find out the related conserved quantities. However, it turns out that such spin chains also possess a few additional conserved quantities which are apparently not derivable from the Lax equations. Identifying these additional conserved quantities, and the usual ones related to Lax equations, with different modes of a monodromy matrix, it is shown that the above mentioned HS like spin chains exhibit multi-parameter deformed and `nonstandard' variants of $Y(gl_M)$ Yangian symmetry.Comment: 18 pages, latex, no figure

Destabilization of the thermohaline circulation by transient perturbations to the hydrological cycle

We reconsider the problem of the stability of the thermohaline circulation as described by a two-dimensional Boussinesq model with mixed boundary conditions. We determine how the stability properties of the system depend on the intensity of the hydrological cycle. We define a two-dimensional parameters' space descriptive of the hydrology of the system and determine, by considering suitable quasi-static perturbations, a bounded region where multiple equilibria of the system are realized. We then focus on how the response of the system to finite-amplitude surface freshwater forcings depends on their rate of increase. We show that it is possible to define a robust separation between slow and fast regimes of forcing. Such separation is obtained by singling out an estimate of the critical growth rate for the anomalous forcing, which can be related to the characteristic advective time scale of the system.Comment: 37 pages, 8 figures, submitted to Clim. Dy

On an exactly solvable BNB_N type Calogero model with nonhermitian PT invariant interaction

An exactly solvable many-particle quantum system is proposed by adding some nonhermitian but PT invariant interactions to the $B_N$ Calogero model. We have shown that such extended $B_N$ Calogero model leads to completely real spectrum which obey generalised exclusion statistics. It is also found that the corresponding exchange statistics parameter exhibit `reflection symmetry' provided the strength of a PT invariant interaction exceeds a critical value.Comment: Revtex, 13 pages, No figures, Minor changes, Version to appear in Phys. Lett

Haldane's Fractional Exclusion Statistics for Multicomponent Systems

The idea of fractional exclusion statistics proposed by Haldane is applied to systems with internal degrees of freedom, and its thermodynamics is examined. In case of one dimension, various bulk quantities calculated show that the critical behavior of such systems can be described by $c=1$ conformal field theories and conformal weights are completely characterized by statistical interactions. It is also found that statistical interactions have intimate relationship with a topological order matrix in Chern-Simons theory for the fractional quantum Hall effect.Comment: 12 pages, Revtex, preprint YITP/K-107