Characterization of chick pea <Emphasis Type="Italic">(Cicer arietum L)</Emphasis> pastes using squeezing flow viscometry

Domestic type and commercial chickpea pastes ('humus'), as well as a commercial soy substitute, were squeezed at a constant displacement rate between 150 mm parallel Teflon plates, mounted on an Instron Universal Testing Machine, before and after stirring. At 1 mm height the crosshead was stopped and the stress relaxation followed. The apparent stress at 1 mm height and that after 1 and 2 min relaxation were considered consistency measures of the pastes. They were reproducible parameters, and sensitive enough to monitor differences between the products, batches of the same product and stirred and unstirred samples. A stronger consistency was reflected not only by a high apparent compressive stress before and after relaxation but also in a higher yield stress, as determined in shear with a parallel plates sensor, suggesting that the paste's texture is determined by a solid like matrix. Stirring invariably reduced the pastes consistency presumably by an irreversible disruption of their microstructure. The presence of suspended solid particles had little or no effect on the pastes ability to retain their consistency after stirring.     

Effect of non-homogeneous surface viscosity on the Marangoni migration of a droplet in viscous fluid

Marangoni migration of a single droplet in an unbounded viscous fluid under the additional effect of variable surface viscosity is studied. The surface tension and the surface viscosity depend on concentration of dissolved species. Cases of the motion induced by the presence of a point source and by a given constant concentration gradient are considered. The dependence of the migration velocity on the governing parameters is computed under quasi-stationary approximation. The effect of weak advective transport is studied making use of singular perturbations in the Peclet number, Pe. It is shown that, when the source is time dependent a Basset-type history term appears in the expansion of the concentration and, as a result, the leading order correction to the flow and to the migration velocity is of O(Pe(1/2)). If the source of active substance driving the flow is steady, the effect of convective transport on the migration is weaker.     

Arithmetic Groups,Base Change,and Representation Growth

Consider an arithmetic group \({\mathbf{G}(O_S)}\), where \({\mathbf{G}}\) is an affine group scheme with connected, simply connected absolutely almost simple generic fiber, defined over the ring of S-integers O _S of a number field K with respect to a finite set of places S. For each \({n \in \mathbb{N}}\), let \({R_n(\mathbf{G}(O_S))}\) denote the number of irreducible complex representations of \({\mathbf{G}(O_S)}\) of dimension at most n. The degree of representation growth \({\alpha(\mathbf{G}(O_S)) = \lim_{n \rightarrow\infty}\log R_n(\mathbf{G}(O_S)) / \log n}\) is finite if and only if \({\mathbf{G}(O_S)}\) has the weak Congruence Subgroup Property. We establish that for every \({\mathbf{G}(O_S)}\) with the weak Congruence Subgroup Property the invariant \({\alpha(\mathbf{G}(O_S))}\) is already determined by the absolute root system of \({\mathbf{G}}\). To show this we demonstrate that the abscissae of convergence of the representation zeta functions of such groups are invariant under base extensions \({K{\subset}L}\). We deduce from our result a variant of a conjecture of Larsen and Lubotzky regarding the representation growth of irreducible lattices in higher rank semi-simple groups. In particular, this reduces Larsen and Lubotzky’s conjecture to Serre’s conjecture on the weak Congruence Subgroup Property, which it refines.     

Uniqueness theorems for Fourier transforms

Let Γ be a smooth curve in the plane R², and Λ be any subset of R². When can one recover uniquely a finite measure μ, supported by Γ and absolutely continuous with respect to the arc length measure on Γ, from the restriction to Λ of its Fourier transform? In this note we present two results in the subject, one is concerned with the case when Γ is a circle, and the other with the case when Λ is “close” to a lattice.     

Dense Fast Random Projections and Lean Walsh Transforms

Random projection methods give distributions over k×d matrices such that if a matrix Ψ (chosen according to the distribution) is applied to a finite set of vectors x _i ∈ℝ ^d the resulting vectors Ψx _i ∈ℝ ^k approximately preserve the original metric with constant probability. First, we show that any matrix (composed with a random ±1 diagonal matrix) is a good random projector for a subset of vectors in ℝ ^d . Second, we describe a family of tensor product matrices which we term Lean Walsh. We show that using Lean Walsh matrices as random projections outperforms, in terms of running time, the best known current result (due to Matousek) under comparable assumptions.     

Coalescence-assisted generation of single nanoliter droplets with predefined composition

We demonstrate the generation of highly accurate nanoliter droplets with a predefined composition. This composition control over a single droplet is achieved by merging two droplets with known concentrations and defined volumes. A forced coalescence is accomplished by synchronizing two piezoelectric-based active droplet generators. A microscope-mounted CCD camera is used to record, quantify and monitor the process to assure its high fidelity. The device is disposable, surfactant free, simple to operate and does not require microelectrode fabrication. It delivers a single on-demand droplet with adjustable high resolution mixing ratios up to 9 at a volume range of 1-10 nanoliters. The presented platform offers, for the first time, a means to perform droplet-based high-throughput screening in the nanoliter range.     

The Quadrupole Response of Borromean Bosonic Trimers

The inelastic response of a Borromean trimer composed of three identical bosons is explored. To this end we use the quadrupole approximation as the excitation mechanism of the bosonic system from its ground state. We utilize the hyperspherical-harmonics expansion to solve the Schroedinger equation and the Lorentz integral transform method to calculate the reaction. It is found that the magnitude of the response function and corresponding sum rules increase as a power law when approaching the three-body threshold. It is also found that this increase is governed by unnatural exponents.     

Algebraic Functions in the Wiener Algebra

We study algebraic properties of the Wiener algebra of absolutely convergent power series on the closed unit disc. In particular, we prove a form of Weierstrass preparation for algebraic functions in this algebra.     

Revisiting Landauʼs density theorems for Paley–Wiener spaces

We present a surprisingly simple approach to Landau?s density theorems for sampling and interpolation, which provides stronger versions of these results. In particular, we extend the interpolation theorem to unbounded spectra.     

Quadrupole response of a weakly bound bosonic trimer

The inelastic response of a bosonic trimer is explored in the confines of the Borromean region. To this end we model the interaction between the external field and the bosonic system as a photoabsorptionlike process and study the response of the trimer in the quadrupole approximation. We utilize the hyperspherical-harmonics expansion to solve the Schr?dinger equation and the Lorentz integral transform method to calculate the reaction. It is found that the magnitude of the response function and corresponding sum rules increase exponentially when approaching the 3-body threshold. It is also found that this increase is governed by unnatural exponents. The connection between our results and radio-frequency experiments in ultracold atom systems is made.