Dye lasing in optically manipulated liquid aerosols

We report lasing in airborne, rhodamine B-doped glycerol-water droplets with diameters ranging between 7.7 and 11.0 mu m, which were localized using optical tweezers. While being trapped near the focal point of an infrared laser, the droplets were pumped with a Q-switched green laser. Our experiments revealed nonlinear dependence of the intensity of the droplet whispering gallery modes (WGMs) on the pump laser fluence, indicating dye lasing. The average wavelength of the lasing WGMs could be tuned between 600 and 630 nm by changing the droplet size. These results may lead to new ways of probing airborne particles, exploiting the high sensitivity of stimulated emission to small perturbations in the droplet laser cavity and the gain medium

Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices

We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three, four or five, where one of the outmost vertices is not covered when the number of vertices $v(n)$ is an odd number. The entropy of absorption of diatomic molecules per site, defined as $S_{SG_d}=\lim_{n \to \infty} \ln N_d(n)/v(n)$, is calculated to be $\ln(2)/3$ exactly for $SG_2(n)$. The numbers of dimers on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4,5$ are also obtained exactly. Their entropies are equal to $\ln(6)/7$, $\ln(28)/12$, $\ln(200)/18$, respectively. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for $SG_d(n)$ with $d=3,4,5$. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of $S_{SG_d}$ with $d=3,4,5$ can be evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl

Spanning Trees on Graphs and Lattices in d Dimensions

The problem of enumerating spanning trees on graphs and lattices is considered. We obtain bounds on the number of spanning trees $N_{ST}$ and establish inequalities relating the numbers of spanning trees of different graphs or lattices. A general formulation is presented for the enumeration of spanning trees on lattices in $d\geq 2$ dimensions, and is applied to the hypercubic, body-centered cubic, face-centered cubic, and specific planar lattices including the kagom\'e, diced, 4-8-8 (bathroom-tile), Union Jack, and 3-12-12 lattices. This leads to closed-form expressions for $N_{ST}$ for these lattices of finite sizes. We prove a theorem concerning the classes of graphs and lattices ${\cal L}$ with the property that $N_{ST} \sim \exp(nz_{\cal L})$ as the number of vertices $n \to \infty$, where $z_{\cal L}$ is a finite nonzero constant. This includes the bulk limit of lattices in any spatial dimension, and also sections of lattices whose lengths in some dimensions go to infinity while others are finite. We evaluate $z_{\cal L}$ exactly for the lattices we considered, and discuss the dependence of $z_{\cal L}$ on d and the lattice coordination number. We also establish a relation connecting $z_{\cal L}$ to the free energy of the critical Ising model for planar lattices ${\cal L}$.Comment: 28 pages, latex, 1 postscript figure, J. Phys. A, in pres

Two-frequency shell model for hypernuclei and meson-exchange hyperon-nucleon potentials

A two-frequency shell model is proposed for investigating the structure of hypernuclei starting with a hyperon-nucleon potential in free space. In a calculation using the folded-diagram method for Λ¹⁶O, the Λ single particle energy is found to have a saturation minimum at an oscillator frequency ħωΛ≈10MeV, for the Λ orbit, which is considerably smaller than ħωN=14MeV for the nucleon orbit. The spin-dependence parameters derived from the Nijmegen NSC89 and NSC97f potentials are similar, but both are rather different from those obtained with the Jülich-B potential. The ΛNN three-body interactions induced by ΛN-ΣN transitions are important for the spin parameters, but relatively unimportant for the low-lying states of Λ¹⁶O.Yiharn Tzeng, S. Y. Tsay Tzeng, T. T. S. Kuo, T.-S.H. Lee, and V. G. D. Stok

Influence of realistic parameters on state-of-the-art LWFA experiments

We examine the influence of non-ideal plasma-density and non-Gaussian transverse laser-intensity profiles in the laser wakefield accelerator analytically and numerically. We find that the characteristic amplitude and scale length of longitudinal density fluctuations impacts on the final energies achieved by electron bunches. Conditions that minimize the role of the longitudinal plasma density fluctuations are found. The influence of higher order Laguerre-Gaussian laser pulses is also investigated. We find that higher order laser modes typically lead to lower energy gains. Certain combinations of higher order modes may, however, lead to higher electron energy gains.Comment: 16 pages, 6 figures; Accepted for publication in Plasma Physics and Controlled Fusio

Spanning trees on the Sierpinski gasket

We obtain the numbers of spanning trees on the Sierpinski gasket $SG_d(n)$ with dimension $d$ equal to two, three and four. The general expression for the number of spanning trees on $SG_d(n)$ with arbitrary $d$ is conjectured. The numbers of spanning trees on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4$ are also obtained.Comment: 20 pages, 8 figures, 1 tabl

Portable Inter-workgroup Barrier Synchronisation for GPUs

Despite the growing popularity of GPGPU programming, there is not yet a portable and formally-specified barrier that one can use to synchronise across workgroups. Moreover, the occupancy-bound execution model of GPUs breaks assumptions inherent in traditional software execution barriers, exposing them to deadlock. We present an occupancy discovery protocol that dynamically discovers a safe estimate of the occupancy for a given GPU and kernel, allowing for a starvation-free (and hence, deadlock-free) inter-workgroup barrier by restricting the number of workgroups according to this estimate. We implement this idea by adapting an existing, previously non-portable, GPU inter-workgroup barrier to use OpenCL 2.0 atomic operations, and prove that the barrier meets its natural specification in terms of synchronisation. We assess the portability of our approach over eight GPUs spanning four vendors, comparing the performance of our method against alternative methods. Our key findings include: (1) the recall of our discovery protocol is nearly 100%; (2) runtime comparisons vary substantially across GPUs and applications; and (3) our method provides portable and safe inter-workgroup synchronisation across the applications we study

Novel pulsatile-release microparticles for single-injection vaccination

Many controlled release devices are designed to achieve near zero-order release kinetics, however for some applications, such as vaccination, non-continuous or pulsatile release is desired. Such pulsatile release systems may enable the creation of single-injection vaccines that eliminate the need for subsequent booster immunizations by spontaneously releasing antigen at time points that correspond to normal vaccination regimens. This would be especially important in the developing world where a lack of consistent access to healthcare contributes to approximately 1.5 million vaccine-preventable deaths each year.1 Here we present the fabrication and characterization of biodegradable core-shell microparticles that exhibit pulsatile release kinetics due to their unique structure. These particles are produced using a novel fabrication process that combines soft lithography, picoliter dispensing, optical alignment, and a gentle heat-based sintering step to generate microparticles with a biodegradable polymeric shell surrounding an antigen-filled core. By altering the composition (e.g. copolymer ratio or molecular weight) of the poly(lactic-co-glycolic acid) shell, particles can be tuned to release discrete pulses of a model antigen at times ranging from four days to two months. This fabrication method is also compatible with sensitive biologics, such as the inactivated polio virus, which retains \u3e80% of its antigenicity after encapsulation. Further, because the shell of the particle is physically separated from the core, these particles can be filled with any aqueous vaccine solution without affecting release kinetics and be easily scaled via massively parallel fabrication. As a result, these particles have exciting potential as single-injection vaccines that fully mimic the antigen presentation profile of traditional bolus injections administered over the course of months or years. Please click Additional Files below to see the full abstract

Probabilistic Bisimulation: Naturally on Distributions

In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a long-standing open problem concerning the representation of memoryless continuous time by memory-full continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems