We present an extensive direct numerical simulation of statistically steady, homogeneous, isotropic turbulence in two-dimensional, binary-fluid mixtures with air-drag-induced friction by using the Cahn-Hilliard-Navier-Stokes equations. We choose parameters, e.g., the surface tension, such that we have a droplet of the minority phase moving inside a turbulent background of the majority phase. We characterize the deformation of the droplet and show that it displays multifractal dynamics. The probability distribution functions of the components of the acceleration of the center of mass of the droplet exhibit wide, non-Gaussian tails. Our study reveals that the droplet enhances the energy spectrum $E(k)$ when the wavenumber $k$ is large; this enhancement leads to dissipation reduction.

AbstractIdentifying effective instructional approaches that stimulate students’ critical thinking (CT) has been the focus of a large body of empirical research. However, there is little agreement on the instructional principles and procedures that are theoretically sound and empirically valid to developing both domain-specific and domain-general CT skills. The purpose of this study was to examine the effectiveness of systematically designed subject matter instruction in stimulating the development of domain-specific and domain-general CT skills, and to investigate the relationship between the two. The study employed a pretest–posttest quasi-experimental design with two conditions: 45 students participated in an experimental condition and 44 students in a control condition. A learning environment, in the context of a freshman physics course, was designed according to the First Principles of Instruction model. The experimental condition followed the designed learning environment, while the control condition followed regular subject matter instruction that was not designed according to the First Principles of Instruction model. The experimental condition scored significantly higher than the control condition on a domain-specific CT test. The results also showed that better performance on a domain-specific CT test explained a significant proportion of the variance on a domain-general CT test. However, the experimental learning environment did not result in a significantly greater pretest–posttest improvement in the acquisition of domain-general CT skills compared to the control learning environment. Instructional design principles that may contribute to the present understanding of the integration of CT skills within the regular subject matter instruction are discussed.

We give examples of rank-one transformations that are (weak) doubly ergodic and rigid (so all their cartesian products are conservative), but with non-ergodic $2$-fold cartesian product. We give conditions for rank-one infinite measure-preserving transformations to be (weak) doubly ergodic and for their $k$-fold cartesian product to be conservative. We also show that a (weak) doubly ergodic nonsingular group action is ergodic with isometric coefficients, and that the latter strictly implies W measurable sensitivity.

Ever since the pioneering work of Bardeen, Cooper and Schrieffer in the 1950s, exploring novel pairing mechanisms for fermion superfluids has become one of the central tasks in modern physics. Here, we investigate a new type of fermion superfluid with hybridized $s$- and $p$-wave pairings in an ultracold spin-1/2 Fermi gas. Its occurrence is facilitated by the co-existence of comparable $s$- and $p$-wave interactions, which is realizable in a two-component $^{40}$K Fermi gas with close-by $s$- and $p$-wave Feshbach resonances. The hybridized superfluid state is stable over a considerable parameter region on the phase diagram, and can lead to intriguing patterns of spin densities and pairing fields in momentum space. In particular, it can induce a phase-locked $p$-wave pairing in the fermion species that has no $p$-wave interactions. The hybridized nature of this novel superfluid can also be confirmed by measuring the $s$-wave and $p$-wave contacts, which can be extracted from the high-momentum tail of the momentum distribution of each spin component. These results enrich our knowledge of pairing superfluidity in Fermi systems, and open the avenue for achieving novel fermion superfluids with multiple partial-wave scatterings in cold atomic gases.

A device that achieves controllable rotation of the state of polarization by rotating the orientation of the eigenmodes of a waveguide by 45$^{\circ}$ is introduced and analyzed. The device can be implemented using lossless materials on a nanoscale and helps circumvent the inherent polarization dependence of photonic devices realized within the silicon on insulator platform. We propose and evaluate two novel polarization rotator-based schemes to achieve polarization engineering functions: (1) A multi-purpose device, with dimensions on the order of a few wavelengths which can function as a polarization splitter or an arbitrary linear polarization state generator. (2) An energy efficient optical modulator that utilizes eigenmode rotation and epsilon near zero (ENZ) effects to achieve high extinction ratio, polarization insensitive amplitude modulation without the need to sweep the device geometry to match the TE and TM mode attributes. By using indium tin oxide (ITO) as an example for a tunable material, the proposed modulator provides polarization insensitive operation and can be realized with a modulation bandwidth of 112 GHz, a length of 1800 nm an energy per bit of 7.5 $fJ$ and an optical bandwidth of 210 nm.

A computationally efficient method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. The method formally discretizes the incompressible Navier-Stokes equations on an unbounded staggered Cartesian grid. Operations are limited to a finite computational domain through a lattice Green's function technique. This technique obtains solutions to inhomogeneous difference equations through the discrete convolution of source terms with the fundamental solutions of the discrete operators. The differential algebraic equations describing the temporal evolution of the discrete momentum equation and incompressibility constraint are numerically solved by combining an integrating factor technique for the viscous term and a half-explicit Runge-Kutta scheme for the convective term. A projection method that exploits the mimetic and commutativity properties of the discrete operators is used to efficiently solve the system of equations that arises in each stage of the time integration scheme. Linear complexity, fast computation rates, and parallel scalability are achieved using recently developed fast multipole methods for difference equations. The accuracy and physical fidelity of solutions is verified through numerical simulations of vortex rings.

The ordering problem in quantum systems with position-dependent mass (PDM) is treated by inclusion of the classically fictitious similarity transformation into the kinetic term. This provides a generation of supersymmetry with the first order supercharges from the kinetic term alone, while inclusion of the potential term allows also to generate nonlinear supersymmetry with higher order supercharges. A broad class of finite-gap systems with PDM is obtained by different reduction procedures, and general results on supersymmetry generation are applied to them. We show that elliptic finite-gap systems of Lame and Darboux-Treibich-Verdier types can be obtained by reduction to Seiffert's spherical spiral and Bernoulli lemniscate in the presence of Calogero-like or harmonic oscillator potentials, or by angular momentum reduction of a free motion on some AdS_2-related surfaces in the presence of Aharonov-Bohm flux. The limiting cases include the Higgs and Mathews-Lakshmanan oscillator models as well as a reflectionless model with PDM exploited recently in the discussion of cosmological inflationary scenarios.

AbstractShiga toxin-producing Escherichia coli O157:H7 ( E. coli O157:H7) strains are foodborne infectious agents that cause a number of life-threatening diseases, including hemorrhagic colitis (HC) and hemolytic uremic syndrome (HUS). Shiga toxin 1 (stx1), shiga toxin 2 (stx2), or a combination of both are responsible for most clinical symptoms of these diseases. Hence, various diagnostic methods have been developed so far to detect shiga toxins such as cell culture, ELISA, Rapid Latex Agglutination (RPLA) and hybridization, but due to high costs and labor time in addition to low sensitivity, they have not received much attention. The aim of this study was to develop a complete, rapid and reliable multiplex PCR (mPCR) method by using two pairs of specific primers to detect either the stx1 or the stx2 gene confirms the presence of E.coli O157:H7. The study results show that stx 1F/ stx 1R primers are specific for stx1 and primers stx 2F/ stx 2R are specific for stx2 genes in E. coli O157:H7. The mPCR method with two pairs of primers for amplifying the stx 1, stx 2 target genes to detect E. coli O157:H7 in food has been set up successfully. Complete method performed well in both types of food matrices with a detection limit of 3 CFU/25 g or mL of food samples. Tests on 180 food samples have shown a specificity value of 93.75 % (95 % confidence interval [CI], 82.83–100), a sensitivity of 100 % (95 % CI, 83.79–99.85 %), and an accuracy of 96.66 % (CI 95 %, 83.41–99.91 %). Interestingly, results indicate that the mPCR performed as well as the traditional culture methods and can reduce the diagnosis time to 2 days. Finally, complete mPCR method was applied to natural samples covering a wide variety of food types proving that the mPCR method was a rapid and reliable screening method for detection of E. coli O157:H7 in food and environmental samples.

This paper reviews the economic and theoretical foundations of insolvency risk measurement and capital adequacy rules. The proposed new measure of insolvency risk is constructed by disentangling assets, debt and equity at the micro-prudential firm level. This new risk index is the Firm Insolvency Risk Index (FIRI) which is symmetrical, proportional and scale invariant. We demonstrate that the balance sheet can be shown to evolve with a fractal pattern. As such we construct a fractal index that can measure the risk of assets. This index can differentiate between the similarity and dissimilarity in asset risk, and it will also possess the properties of being self-similar and invariant to firm characteristics that make up its asset composition hence invariant to all types of risk derived from assets. Self-similarity and scale invariance across the cross section allows direct comparison of degrees of risk in assets. This is by comparing the risk dissimilarity of assets. Being naturally bounded to its highest upper bound, (0,2], the fractal index is able to serve like a risk thermometer. We assign geometric probabilities of insolvency P (equity is equal or less than 0 conditional on debt being greater than 0).

We show that a scalar field without a kinetic term in the Lagrangian density, coupled to the covariant divergence of the torsion vector in the Einstein$-$Cartan theory of gravity, becomes kinetic in its general-relativistic equivalent formulation. The resulting kinetic term is negative: such a scalar field could be a source of phantom dark energy.