Experimental demonstration of PT‐symmetric stripe lasers

Recently, the coexistence of a parity‐time (PT) symmetric laser and absorber has gained tremendous research attention. While PT‐symmetric lasers have been observed in microring resonators, the experimental demonstration of a PT‐symmetric stripe laser is still absent. Here, we experimentally study a PT‐symmetric laser absorber in a stripe waveguide. Using the concept of PT‐symmetry to exploit the light amplification and absorption, PT‐symmetric laser absorbers have been successfully obtained. In contrast to the single‐mode PT‐symmetric lasers, the PT‐symmetric stripe lasers have been experimentally confirmed by comparing the relative wavelength positions and mode spacing under different pumping conditions. When the waveguide is half‐pumped, the mode spacing is doubled and the lasing wavelengths shift to the center of every two initial lasing modes. All these observations are consistent with the theoretical predictions and well confirm the PT‐symmetry breaking.

     

Energy transfer of highly vibrationally excited azulene. II. Photodissociation of azulene-Kr van der Waals clusters at 248 and 266 nm

Photodissociation of azulene-Kr van der Waals clusters at 266 and 248 nm was studied using velocity map ion imaging techniques with the time-sliced modification. Scattered azulene molecules produced from the dissociation of clusters were detected by one-photon vacuum ultraviolet ionization. Energy transfer distribution functions were obtained from the measurement of recoil energy distributions. The distribution functions can be described approximately by multiexponential functions. Fragment angular distributions were found to be isotropic. The energy transfer properties show significantly different behavior from those of bimolecular collisions. No supercollisions were observed under the signal-to-noise ratios S/N=400 and 100 at 266 and 248 nm, respectively. Comparisons with the energy transfer of bimolecular collisions in thermal systems and the crossed-beam experiment within detection limit are made.     

A nonuniform L2 formula of Caputo derivative and its application to a fractional Benjamin–Bona–Mahony-type equation with nonsmooth solutions

To recover the full accuracy of discretized fractional derivatives, nonuniform mesh technique is a natural and simple approach to efficiently resolve the initial singularities that always appear in the solutions of time-fractional linear and nonlinear differential equations. We first construct a nonuniform L2 approximation for the fractional Caputo's derivative of order 1 < α < 2 and present a global consistency analysis under some reasonable regularity assumptions. The temporal nonuniform L2 formula is then utilized to develop a linearized difference scheme for a time-fractional Benjamin–Bona–Mahony-type equation. The unconditional convergence of our scheme on both uniform and nonuniform (graded) time meshes are proven with respect to the discrete H¹-norm. Numerical examples are provided to justify the accuracy.     

Super-strong RKA secure MAC,PKE and SE from tag-based hash proof system

\(\mathcal {F}\)-related-key attacks (RKA) on cryptographic systems consider adversaries who can observe the outcome of a system under not only the original key, say k, but also related keys f(k), with f adaptively chosen from \(\mathcal {F}\) by the adversary. In this paper, we define new RKA security notions for several cryptographic primitives including message authentication code (MAC), public-key encryption (PKE) and symmetric encryption (SE). This new kind of RKA notions are called super-strong RKA securities, which stipulate minimal restrictions on the adversary’s forgery or oracle access, thus turn out to be the strongest ones among existing RKA security requirements. We present paradigms for constructing super-strong RKA secure MAC, PKE and SE from a common ingredient, namely Tag-based hash proof system (THPS). We also present constructions for THPS based on the k-linear and the DCR assumptions. When instantiating our paradigms with concrete THPS constructions, we obtain super-strong RKA secure MAC, PKE and SE schemes for the class of restricted affine functions \(\mathcal {F}_{\text {raff}}\), of which the class of linear functions \(\mathcal {F}_{\text {lin}}\) is a subset. To the best of our knowledge, our MACs, PKEs and SEs are the first ones possessing super-strong RKA securities for a non-claw-free function class \(\mathcal {F}_{\text {raff}}\) in the standard model and under standard assumptions. Our constructions are free of pairing and are as efficient as those proposed in previous works. In particular, the keys, tags of MAC and ciphertexts of PKE and SE all consist of only a constant number of group elements.     

A linearized second-order scheme for nonlinear time fractional Klein-Gordon type equations

We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. A linearized scheme is proposed to solve the problem. As a result, iterative method need not be employed. One of the main difficulties for the analysis is that certain weight averages of the approximated solutions are considered in the discretization and standard energy estimates cannot be applied directly. By introducing a new grid function, which further approximates the solution, and using ideas in some recent studies, we show that the method converges with second-order accuracy in time.     

Synthesis of high-quality single-walled carbon nanotubes by catalytic decomposition of C2H2

High-quality single-walled carbon nanotubes free of defects and amorphous carbon coating have been produced by catalytic decomposition of C2H2 over Fe-Mo/Al2O3 catalyst.     

Composites prepared by penetrating poly(ethylene oxide) chains into mesoporous silica

Mesoporous silica was synthesized by hydrolysis of tetraethylorthosilicate (TEOS, formula Si(OCH₂CH₃)₄) at ambient temperature in a basic ethanol-water solution, with cetyltrimethyl ammonium bromide as a template. It had a surface area of approximately 1,400 m²/g, and an average pore diameter of approximately 40 Å. Portions were blended into three samples of poly(ethylene oxide) (PEO) of varying molecular weights, in the hope of making novel composites by penetrating some of the PEO chains into the silica channels. Differential Scanning Calorimetry (DSC) and X-ray diffraction (XRD) were used to characterize the structures of the PEO/mesoporous silica composites after they were held at 100 °C for up to 30 min. In both experiments, the melting temperature of the PEO decreased and ultimately disappeared. These results suggest that the PEO chains did penetrate into the silica pores, and since they were constrained in the pores, their crystallization was suppressed. This provides an interesting parallel to the disappearance of the glass transition temperatures of polymers constrained in the cavities of zeolites or in the galleries of intercalated clays.     

Electrogenerated Chemiluminescence Ethanol Biosensor Based on Carbon Nanotube‐Titania‐Nafion Composite Film

Mesoporous titania‐Nafion composite doped with carbon nanotube (CNT) has been used for the immobilization of tris(2,2′‐bipyridyl)ruthenium(II) (Ru(bpy)₃²⁺) and alcohol dehydrogenase on an electrode surface to yield a highly sensitive and stable electrogenerated chemiluminescence (ECL) ethanol biosensor. The presence of CNT in the composite film increases not only the sensitivity of the ECL biosensor but also the long‐term stability of the biosensor. The present biosensor responds linearly to ethanol in the wide concentration ranges from 1.0×10^?5 M to 1.0×10^?1 M with a detection limit of 5.0×10^?6 M (S/N=3). The present ECL ethanol biosensor exhibited higher ECL response compared to that obtained with the ECL biosensor based on the corresponding composite without CNT. The present CNT‐based ECL biosensor showed good long‐term stability with 75% of its initial activity retained after 2 weeks of storage in 50 mM phosphate buffer at pH 7.0.     

Analytical solutions to mathematical models of the surface and bulk erosion of solid polymers

The process by which polymeric materials hydrolyze and disappear into their environments is often called erosion. Two types of erosion have been defined according to how the hydrolysis takes place. If hydrolysis occurs throughout the entire specimen at the same time, it is called bulk erosion. If the hydrolysis is mainly confined to a region near the surface of the specimen and the surface continuously degrades by moving inward, it is termed surface erosion. In this article, a kinetic relationship for bulk erosion is developed. This relationship provides a method for estimating the hydrolysis kinetic constants for bulk‐eroding polymers. This same relationship is also applicable to surface erosion at a microscopic level. Through its combination with a diffusion–reaction equation and the provision of moving boundary conditions, an analytical solution to the steady‐state surface‐erosion problem is obtained. The erosion rate, erosion front width, and induction time can all be expressed as simple functions of the rate of polymer bond hydrolysis, water diffusivity, and solubility, plus other parameters that can be experimentally determined. The erosion front width is the product of the induction time and the erosion rate. The ratio of the erosion front width to the polymer specimen thickness is a parameter that determines whether the specimen undergoes surface or bulk erosion. Theoretical results are compared with experimental observations from the literature, and agreement is found. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 383–397, 2005